Produção Nacional
Revisado por pares
On a p(x)-Kirchhoff equation with critical exponent and an additional nonlocal term via truncation argument
2015; Wiley; Volume: 288; Issue: 11-12 Linguagem: Inglês
10.1002/mana.201400198
ISSN1522-2616
AutoresFrancisco Júlio S. A. Corrêa, Augusto César dos Reis Costa,
Tópico(s)Advanced Mathematical Modeling in Engineering
ResumoMathematische NachrichtenVolume 288, Issue 11-12 p. 1226-1240 Original Paper On a -Kirchhoff equation with critical exponent and an additional nonlocal term via truncation argument Francisco Julio S. A. Corrêa, Francisco Julio S. A. Corrêa [email protected] +55 83 2101 1112 | Fax: +55 83 2101 1112 Universidade Federal de Campina Grande, Centro de Ciências e Tecnologia, Unidade Acadêmica de Matemática, CEP 58.109-970 Campina Grande, PB, BrazilSearch for more papers by this authorAugusto César dos Reis Costa, Corresponding Author Augusto César dos Reis Costa Universidade Federal de Campina Grande, Centro de Ciências e Tecnologia, Unidade Acadêmica de Matemática, CEP 58.109-970 Campina Grande, PB, Brazil Universidade Federal do Pará, Instituto de Ciências Exatas e Naturais, Faculdade de Matemática, CEP 66075-110 Belém, PA, BrazilCorresponding author: e-mail: [email protected], Phone: +55 91 3201 7415, Fax: +55 91 3201 7415Search for more papers by this author Francisco Julio S. A. Corrêa, Francisco Julio S. A. Corrêa [email protected] +55 83 2101 1112 | Fax: +55 83 2101 1112 Universidade Federal de Campina Grande, Centro de Ciências e Tecnologia, Unidade Acadêmica de Matemática, CEP 58.109-970 Campina Grande, PB, BrazilSearch for more papers by this authorAugusto César dos Reis Costa, Corresponding Author Augusto César dos Reis Costa Universidade Federal de Campina Grande, Centro de Ciências e Tecnologia, Unidade Acadêmica de Matemática, CEP 58.109-970 Campina Grande, PB, Brazil Universidade Federal do Pará, Instituto de Ciências Exatas e Naturais, Faculdade de Matemática, CEP 66075-110 Belém, PA, BrazilCorresponding author: e-mail: [email protected], Phone: +55 91 3201 7415, Fax: +55 91 3201 7415Search for more papers by this author First published: 16 March 2015 https://doi.org/10.1002/mana.201400198Citations: 7Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract We study existence and multiplicity of solutions of the following nonlocal -Kirchhoff equation with critical exponent, via truncation argument on the Sobolev space with variable exponent, where Ω is a bounded smooth domain of , , M, f are continuous functions, , and are real parameter. References 1A. Ambrosetti and A. Malchiodi, Nonlinear Analysis and Semilinear Elliptic Problems, Cambridge Stud. Adv. Math. Vol. 14 (Cambridge University Press, Cambridge, 2007). Google Scholar 2G. Autuori and P. Pucci, Kirchhoff systems with nonlinear source and boundary damping terms, Commun. Pure Appl. Anal. 9, 1161–1188 (2010). 10.3934/cpaa.2010.9.1161 Web of Science®Google Scholar 3J. G. Azorero and I. P. Alonso, Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term, Trans. Amer. Math. Soc. 323, 877–895 (1991). 10.2307/2001562 Web of Science®Google Scholar 4J. F. Bonder and A. Silva, The concentration compactness principle for variable exponent spaces and application, Eletron. J. Differential Equations 2010(141), 1–18 (2010). Google Scholar 5A. Castro, Métodos Variacionales en Análisis Functional no Linear, monograph published by the Colombian Math. Soc. (1980). Google Scholar 6M. Chipot, Elements of Nonlinear Analysis, Birkhäuser Advanced Texts (Birkhäuser, Basel, 2000). 10.1007/978-3-0348-8428-0 Google Scholar 7D. C. Clark, A variant of the Lusternik-Schnirelman theory, Indiana Univ. Math. J. 22, 65–74 (1972). 10.1512/iumj.1973.22.22008 Web of Science®Google Scholar 8F. J. S. A. Corrêa, M. Delgado, and A. Suárez, A variational approach to a nonlocal elliptic problem with sign-changing nonlinearity, Advanced Nonlinear Studies 11, 361–375 (2011). Web of Science®Google Scholar 9F. J. S. A. Corrêa and G. M. Figueiredo, On an elliptic equation of p-Kirchhof type via variational methods, Bull. Aust. Math. Soc. 74, 263–277 (2006). 10.1017/S000497270003570X Web of Science®Google Scholar 10D. G. Costa, Tópicos em Análise não-Linear e Aplicações às Equações Diferenciais, A VIII Escola Latino-Americana de Matemática (IMPA, Rio de Janeiro, RJ, Brazil, 1986). Google Scholar 11X. Fan, On nonlocal p(x)-Laplacian Dirichlet problems, Nonlinear Anal. 72, 3314–3323 (2010). 10.1016/j.na.2009.12.012 Web of Science®Google Scholar 12X. L. Fan, J. S. Shen, and D. Zhao, Sobolev embedding theorems for spaces , J. Math. Anal. Appl. 262, 749–760 (2001). 10.1006/jmaa.2001.7618 Web of Science®Google Scholar 13X. L. Fan and Q. H. Zhang, Existence of solutions for p(x)-Laplacian Dirichlet problems, Nonlinear Anal. 52, 1843–1852 (2003). 10.1016/S0362-546X(02)00150-5 Web of Science®Google Scholar 14X. L. Fan and D. Zhao, On the spaces and , J. Math. Anal. Appl. 263, 424–446 (2001). 10.1006/jmaa.2000.7617 Web of Science®Google Scholar 15G. M. Figueiredo and J. R. Santos Junior, Multiplicity of solutions for a Kirchhoff equation with subcritical or critical growth, Differential Integral Equations 25(9/10), 853–868 (2012). Web of Science®Google Scholar 16R. Filippucci, P. Pucci, and V. Radulescu, Existence and non-existence results for quasilinear elliptic exterior problems with nonlinear boundary conditions, Comm. Partial Differential Equations 33, 706–717 (2008). 10.1080/03605300701518208 Web of Science®Google Scholar 17J. M. Gomes and L. Sanchez, On a variational approach to some non-local boundary value problems, Applicable Analysis 84(9), 909–925 (2005). 10.1080/00036810500048202 Google Scholar 18M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations (MacMillan, New York, 1964). Web of Science®Google Scholar 19J. L. Lions, Quelques Méthodes de Resolution des Problémes aux Limites non Linéaires (Dunod, Paris, 1969). Google Scholar 20J. L. Lions, On Some Questions in Boundary Value Problems of Mathematical Physics (Instituto de Matemática, UFRJ, Rio de Janeiro, RJ, Brazil, 1978). 10.1016/S0304-0208(08)70870-3 Google Scholar 21P. L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, Rev. Mat. Iberoam. 1, 145–201 (1985). 10.4171/RMI/6 Google Scholar 22G. Molica Bisci and V. Radulescu, Mountain pass solutions for nonlocal equations, Ann. Acad. Sci. Fennicae 39, 579–592 (2014). 10.5186/aasfm.2014.3921 Web of Science®Google Scholar 23X. Shang and Z. Wang, Existence of solutions for dicontinuous -Laplacian problems with critical exponent, Eletron. J. Differential Equations 2012(25), 1–12 (2012). Google Scholar 24F. Yongqiang, The principle of concentration compactness in spaces and its application, Nonlinear Anal. 71, 1876–1892 (2009). 10.1016/j.na.2009.01.023 Web of Science®Google Scholar Citing Literature Volume288, Issue11-12August 2015Pages 1226-1240 ReferencesRelatedInformation
Referência(s)