SOBOLEV VERSUS HÖLDER LOCAL MINIMIZERS AND GLOBAL MULTIPLICITY FOR SOME QUASILINEAR ELLIPTIC EQUATIONS
2000; World Scientific; Volume: 02; Issue: 03 Linguagem: Inglês
10.1142/s0219199700000190
ISSN1793-6683
AutoresJ.P. Garcı́a Azorero, Ireneo Peral, Juan J. Manfredi,
Tópico(s)Advanced Numerical Methods in Computational Mathematics
ResumoCommunications in Contemporary MathematicsVol. 02, No. 03, pp. 385-404 (2000) No AccessSOBOLEV VERSUS HÖLDER LOCAL MINIMIZERS AND GLOBAL MULTIPLICITY FOR SOME QUASILINEAR ELLIPTIC EQUATIONSJ. P. GARCÍA AZORERO, I. PERAL ALONSO, and JUAN J. MANFREDIJ. P. GARCÍA AZORERODepartamento de Matemáticas Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain, I. PERAL ALONSODepartamento de Matemáticas Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain, and JUAN J. MANFREDIDepartment of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USAhttps://doi.org/10.1142/S0219199700000190Cited by:228 Previous AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail First and third authors partially supported by DGICYT project PB97-0052, M.E.C. Spain, second author partially supported by NSF Grant DMS-9501561. Remember to check out the Most Cited Articles! 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Papageorgiou and George Smyrlis13 May 2011 | Positivity, Vol. 16, No. 2W 0 1, P(X) VERSUS C 1 LOCAL MINIMIZERS FOR NONSMOOTH FUNCTIONALSChengfu Che, Bin Ge, Xiao-Ping Xue and Qing-Mei Zhou1 Jun 2012 | Mathematical Modelling and Analysis, Vol. 17, No. 3Nonlinear Elliptic Equations with Singular Terms and Combined NonlinearitiesLeszek Gasiński and Nikolaos S. Papageorgiou9 August 2011 | Annales Henri Poincaré, Vol. 13, No. 3Multiple solutions for asymptotically (p−1) -homogeneous p-Laplacian equationsLeszek Gasiński and Nikolaos S. Papageorgiou1 Mar 2012 | Journal of Functional Analysis, Vol. 262, No. 5Limits as of -Laplacian concave–convex problemsFernando Charro and Ireneo Peral1 Mar 2012 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 75, No. 4Multiple existence results of solutions for the Neumann problems via super- and sub-solutionsShizuo Miyajima, Dumitru Motreanu and Mieko Tanaka1 Feb 2012 | Journal of Functional Analysis, Vol. 262, No. 4Constant sign and nodal solutions for logistic-type equations with equidiffusive reactionNikolaos S. Papageorgiou and Francesca Papalini5 November 2010 | Monatshefte für Mathematik, Vol. 165, No. 1Multiple Positive Solutions for a Quasilinear Elliptic System Involving Concave-Convex Nonlinearities and Sign-Changing Weight FunctionsTsing-San Hsu1 Jan 2012 | International Journal of Mathematics and Mathematical Sciences, Vol. 2012A Bifurcation-Type Result for Nonlinear Neumann Eigenvalue ProblemsSophia Th. Kyritsi and Nikolaos S. Papageorgiou1 Jan 2012 | Funkcialaj Ekvacioj, Vol. 55, No. 1Multiple solutions for Neumann and periodic problems with singular ϕ-LaplacianCristian Bereanu, Petru Jebelean and Jean Mawhin1 Dec 2011 | Journal of Functional Analysis, Vol. 261, No. 11Anisotropic nonlinear Neumann problemsLeszek Gasiński and Nikolaos S. Papageorgiou19 January 2011 | Calculus of Variations and Partial Differential Equations, Vol. 42, No. 3-4Existence of three nontrivial solutions for asymptotically -linear noncoercive -Laplacian equationsNikolaos S. Papageorgiou and Eugénio M. Rocha1 Nov 2011 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 74, No. 16Existence of positive solutions for a class of semilinear and quasilinear elliptic equations with supercritical caseJuanjuan Gao, Yong Zhang and Peihao Zhao1 Sep 2011 | Journal of Mathematical Analysis and Applications, Vol. 381, No. 1Positive solutions for nonlinear periodic problems with concave termsSergiu Aizicovici, Nikolaos S. Papageorgiou and Vasile Staicu1 Sep 2011 | Journal of Mathematical Analysis and Applications, Vol. 381, No. 2A multiplicity theorem for p-superlinear p-Laplacian equations using critical groups and morse theorySophia Th. Kyritsi, Donal O’Regan and Nikolaos S. Papageorgiou23 February 2010 | Monatshefte für Mathematik, Vol. 163, No. 4MULTIPLICITY OF SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS WITH COMBINED NONLINEARITIESXIAO JUN CHANG20 November 2011 | Communications in Contemporary Mathematics, Vol. 13, No. 03A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problemsD. Motreanu, Donal O'Regan and Nikolaos S. Papageorgiou1 May 2011 | Communications on Pure and Applied Analysis, Vol. 10, No. 6Nonlinear Neumann equations driven by a nonhomogeneous differential operatorShouchuan Hu and Nikolaos S. Papageorgiou1 Apr 2011 | Communications on Pure and Applied Analysis, Vol. 10, No. 4Multiple solutions of an even-order nonlinear problem with convex–concave nonlinearityV.F. Lubyshev1 Feb 2011 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 74, No. 4Existence of multiple solutions of higher-order nonlinear elliptic equationsV. F. Lubyshev10 March 2011 | Mathematical Notes, Vol. 89, No. 1-2Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions inTsing-San Hsu1 Jan 2011 | Abstract and Applied Analysis, Vol. 2011Кратная разрешимость нелинейных эллиптических уравнений высокого порядкаВладимир Федорович Лубышев and Vladimir Feodorovich Lubyshev1 Jan 2011 | Математические заметки, Vol. 89, No. 2Sign-changing and constant-sign solutions for p-Laplacian problems with jumping nonlinearitiesDumitru Motreanu and Mieko Tanaka1 Dec 2010 | Journal of Differential Equations, Vol. 249, No. 12Existence and multiplicity of solutions of quasilinear equations with convex or nonconvex reaction termH. A. Hamid and M. F. Bidaut-Veron29 September 2010 | Journal of Mathematical Sciences, Vol. 170, No. 3Nonexistence, existence and multiplicity of positive solutions to the -Laplacian nonlinear Neumann boundary value problemShao-Gao Deng and Qin Wang1 Oct 2010 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 73, No. 7Existence of Multiple Solutions for Nonlinear Dirichlet Problems with a Nonhomogeneous Differential OperatorSophia Th. Kyritsi, Donal O’ Regan and Nikolaos S. Papageorgiou10 March 2016 | Advanced Nonlinear Studies, Vol. 10, No. 3Multiple positive solutions of an elliptic equation with a convex-concave nonlinearity containing a sign-changing termV. F. Lubyshev9 September 2010 | Proceedings of the Steklov Institute of Mathematics, Vol. 269, No. 1Multiple Nontrivial Solutions for a Class of p-Laplacian EquationsLei Wei, Mingxin Wang and Jiang Zhu28 March 2009 | Acta Applicandae Mathematicae, Vol. 110, No. 3Local -minimizers versus local -minimizers of nonsmooth functionalsPatrick Winkert1 Jun 2010 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 72, No. 11Multiple solutions to p-Laplacian problems with concave nonlinearitiesLinsong Shi and Xiaojun Chang1 Mar 2010 | Journal of Mathematical Analysis and Applications, Vol. 363, No. 1W01,p versus C1 local minimizers for a singular and critical functionalJ. Giacomoni and K. Saoudi1 Mar 2010 | Journal of Mathematical Analysis and Applications, Vol. 363, No. 2Multiple positive solutions for a class of -superlinear elliptic problemsSophia Th. Kyritsi and Nikolaos S. Papageorgiou1 Mar 2010 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 72, No. 6Two positive solutions for p -Laplacian equations with convex and concave non-linearities and a non-smooth potentialMichael E. Filippakis and Nikolaos S. Papageorgiou1 Feb 2010 | Applicable Analysis, Vol. 89, No. 2Multiple radial solutions for a class of quasilinear elliptic problemsXiaoming He1 Jan 2010 | Applied Mathematics Letters, Vol. 23, No. 1Positive solutions of the p-Laplacian involving a superlinear nonlinearity with zerosLeonelo Iturriaga, Eugenio Massa, Justino Sánchez and Pedro Ubilla1 Jan 2010 | Journal of Differential Equations, Vol. 248, No. 2Multiple Positive Solutions for Semilinear Elliptic Equations in Involving Concave-Convex Nonlinearities and Sign-Changing Weight FunctionsTsing-San Hsu and Huei-Li Lin1 Jan 2010 | Abstract and Applied Analysis, Vol. 2010Multiple Positive Solutions for a Class of Concave-Convex Semilinear Elliptic Equations in Unbounded Domains with Sign-Changing WeightsTsing-San Hsu1 Jan 2010 | Boundary Value Problems, Vol. 2010, No. 1Multiplicity of solutions for parametric $p$-Laplacian equations with nonlinearity concave near the originShouchuan Hu and Nikolaos S. Papageorgiou1 Jan 2010 | Tohoku Mathematical Journal, Vol. 62, No. 1Positive solutions for Robin problem involving the p(x) -LaplacianShao-Gao Deng1 Dec 2009 | Journal of Mathematical Analysis and Applications, Vol. 360, No. 2Nodal and multiple constant sign solutions for resonant -Laplacian equations with a nonsmooth potentialLeszek Gasiński and Nikolaos S. Papageorgiou1 Dec 2009 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, No. 11Multiplicity of solutions for a quasilinear elliptic problem via the cohomological indexEveraldo Medeiros and Kanishka Perera1 Nov 2009 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, No. 9Multiple positive solutions for a critical quasilinear elliptic system with concave–convex nonlinearitiesTsing-San Hsu1 Oct 2009 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, No. 7-8Nonlinear elliptic equations with an asymptotically linear reaction termNikolaos S. Papageorgiou and George Smyrlis1 Oct 2009 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, No. 7-8Multiple positive solutions for semilinear Dirichlet problems with sign-changing weight function in infinite strip domainsM.L. Miotto and O.H. Miyagaki1 Oct 2009 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, No. 7-8Existence of multiple solutions with precise sign information for superlinear Neumann problemsSergiu Aizicovici, Nikolaos S. Papageorgiou and Vasile Staicu26 February 2009 | Annali di Matematica Pura ed Applicata, Vol. 188, No. 4Local “superlinearity” and “sublinearity” for the p-LaplacianDjairo G. de Figueiredo, Jean-Pierre Gossez and Pedro Ubilla1 Aug 2009 | Journal of Functional Analysis, Vol. 257, No. 3Multiple positive solutions for quasilinear problems with indefinite sublinear nonlinearityFrancisco Odair de Paiva1 Aug 2009 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, No. 3-4Multiple Solutions for Resonant Hemivariational Inequalities via Minimax MethodsSophia Th. Kyritsi, Donal O’ Regan and Nikolaos S. Papageorgiou10 March 2016 | Advanced Nonlinear Studies, Vol. 9, No. 3Multiplicity of solutions to uniformly elliptic fully nonlinear equations with concave–convex right-hand sideFernando Charro, Eduardo Colorado and Ireneo Peral1 Jun 2009 | Journal of Differential Equations, Vol. 246, No. 11Pairs of positive solutions for -Laplacian equations with sublinear and superlinear nonlinearities which do not satisfy the AR-conditionNikolaos S. Papageorgiou and Eugénio M. Rocha1 Jun 2009 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 70, No. 11Multiplicity of solutions for a class of resonant p -Laplacian Dirichlet problemsEvgenia Papageorgiou and Nicolaos Papageorgiou1 Jun 2009 | Pacific Journal of Mathematics, Vol. 241, No. 2Existence of three nontrivial solutions for nonlinear Neumann hemivariational inequalitiesAntonio Iannizzotto and Nikolaos S. Papageorgiou1 May 2009 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 70, No. 9versus local minimizers for elliptic functionals with critical growth inJacques Giacomoni, S. Prashanth and K. Sreenadh1 Mar 2009 | Comptes Rendus Mathematique, Vol. 347, No. 5-6Existence of a non-trivial solution for the p-Laplacian equation with Fučík type resonance at infinityMieko Tanaka1 Mar 2009 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 70, No. 6Multiplicity Results for p -Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight FunctionsTsing-San Hsu1 Jan 2009 | Abstract and Applied Analysis, Vol. 2009Local ‘Superlinearity’ and ‘Sublinearity’ for the p-LaplacianDjairo G. de Figueiredo, Jean-Pierre Gossez and Pedro Ubilla8 January 2014Multiplicity theorems for superlinear elliptic problemsNikolaos S. Papageorgiou, Eugénio M. Rocha and Vasile Staicu13 March 2008 | Calculus of Variations and Partial Differential Equations, Vol. 33, No. 2Multiple constant sign and nodal solutions for nonlinear elliptic equations with the p-LaplacianMichael E. Filippakis and Nikolaos S. Papageorgiou1 Oct 2008 | Journal of Differential Equations, Vol. 245, No. 7Three nontrivial solutions for the -Laplacian with a nonsmooth potentialNikolaos S. Papageorgiou, Sandrina Rafaela Andrade Santos and Vasile Staicu1 Jun 2008 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 68, No. 12A degree theoretic approach for multiple solutions of constant sign for nonlinear elliptic equationsD. Motreanu, V. V. Motreanu and N. S. Papageorgiou1 August 2007 | manuscripta mathematica, Vol. 124, No. 4A multiplicity theorem for the Neumann p-Laplacian with an asymmetric nonsmooth potentialGiuseppina Barletta and Nikolaos S. Papageorgiou21 February 2007 | Journal of Global Optimization, Vol. 39, No. 3Multiple positive solutions for a superlinear elliptic problem in with a sublinear Neumann boundary conditionS. Prashanth and K. Sreenadh1 Aug 2007 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 67, No. 4On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problemsNobuyoshi Fukagai and Kimiaki Narukawa18 August 2006 | Annali di Matematica Pura ed Applicata, Vol. 186, No. 3On the sub-supersolution method for p(x) -Laplacian equationsXianling Fan1 Jun 2007 | Journal of Mathematical Analysis and Applications, Vol. 330, No. 1A multiplicity theorem for problems with the p-LaplacianEvgenia H. Papageorgiou and Nikolaos S. Papageorgiou1 Mar 2007 | Journal of Functional Analysis, Vol. 244, No. 1A global multiplicity result for N-Laplacian with critical nonlinearity of concave-convex typeJ. Giacomoni, S. Prashanth and K. Sreenadh1 Jan 2007 | Journal of Differential Equations, Vol. 232, No. 2Existence and Multiplicity Results for a Degenerate Elliptic EquationWei Dong and Jian Tao Chen14 March 2006 | Acta Mathematica Sinica, English Series, Vol. 22, No. 3Multiple solutions for coercive p-Laplacian equationsShibo Liu1 Apr 2006 | Journal of Mathematical Analysis and Applications, Vol. 316, No. 1Existence and asymptotic behavior of solutions for a class of Neumann problemsIlma Marques1 Sep 2005 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 62, No. 6Existence and multiplicity results for quasilinear elliptic equationsWei Dong17 April 2009 | Bulletin of the Australian Mathematical Society, Vol. 71, No. 3On nonlocal existence results for elliptic equations with convex–concave nonlinearitiesYavdat Il’yasov1 Apr 2005 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 61, No. 1-2Existence and asymptotic behavior of solutions for a class of nonlinear elliptic equations with Neumann conditionIlma Marques1 Apr 2005 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 61, No. 1-2Multiplicity of positive solutions for a class of quasilinear nonhomogeneous Neumann problemsEmerson A.M. Abreu, João Marcos do Ó and Everaldo S. Medeiros1 Mar 2005 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 60, No. 8Existence of Multiple Positive Solutions for N-Laplacian in a Bounded Domain in ℝ NS. Prashanth and K. Sreenadh10 March 2016 | Advanced Nonlinear Studies, Vol. 5, No. 1Multiplicity of positive solutions for p-Laplace equation with superlinear-type nonlinearityS. Prashanth and K. Sreenadh1 Mar 2004 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 56, No. 6Partial differential equations involving subcritical, critical and supercritical nonlinearitiesSebastián Lorca and Pedro Ubilla1 Jan 2004 | Nonlinear Analysis: Theory, Methods & Applications, Vol. 56, No. 1MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS ASSOCIATED TO A CLASS OF p-LAPLACIAN LIKE OPERATORSNOBUYOSHI FUKAGAI and KIMIAKI NARUKAWA20 November 2011 | Communications in Contemporary Mathematics, Vol. 05, No. 05W1,p versus C1 local minimizers and multiplicity results for quasilinear elliptic equationsZongming Guo and Zhitao Zhang1 Oct 2003 | Journal of Mathematical Analysis and Applications, Vol. 286, No. 1Nodal and Multiple Constant Sign Solution for Equations with the p-LaplacianRavi P. Agarwal, Michael E. Filippakis, Donal O’Regan and Nikolaos S. Papageorgiou Recommended Vol. 02, No. 03 Metrics History Received 5 July 1999 PDF download
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