Existence of solutions to nonlinear, subcritical higher order elliptic Dirichlet problems
2009; Elsevier BV; Volume: 248; Issue: 7 Linguagem: Inglês
10.1016/j.jde.2009.09.012
ISSN1090-2732
AutoresWolfgang Reichel, Tobias Weth,
Tópico(s)Differential Equations and Boundary Problems
ResumoWe consider the 2m-th order elliptic boundary value problem Lu=f(x,u) on a bounded smooth domain Ω⊂RN with Dirichlet boundary conditions on ∂Ω. The operator L is a uniformly elliptic linear operator of order 2m whose principle part is of the form (−∑i,j=1Naij(x)∂2∂xi∂xj)m. We assume that f is superlinear at the origin and satisfies lims→∞f(x,s)sq=h(x), lims→−∞f(x,s)|s|q=k(x), where h,k∈C(Ω¯) are positive functions and q>1 is subcritical. By combining degree theory with new and recently established a priori estimates, we prove the existence of a nontrivial solution.
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