Abstract
We use Minimax Methods and explore compact embedddings in the context of Orlicz and Orlicz‐Sobolev spaces to get existence of weak solutions on a class of semilinear elliptic equations with nonlinearities near critical growth. We consider both biharmonic equations with Navier boundary conditions and Laplacian equations with Dirichlet boundary conditions.
Highlights
We use Minimax Methods and explore compact embedddings in the context of Orlicz and Orlicz-Sobolev spaces to get existence of weak solutions on a class of semilinear elliptic equations with nonlinearities near critical growth
Our concern in this paper is on finding weak solutions for the problem (--1)’A’u f(x,u) in B,(u)=O on OR
B=() (, (m- l)&), that is, B() 0 means either the Dirichlet or the Navier boundary conditions according to m=lorm=2
Summary
Our concern in this paper is on finding weak solutions for the problem (--1)’A’u f(x,u) in B,(u)=O on OR (1.1). 0 and the boundary operator B is given by is a bounded domain with smith boundary. B=() (, (m- l)&), that is, B() 0 means either the Dirichlet or the Navier boundary conditions according to m=lorm=2. By a weak solution of (i.I) we mean n element E H= HJ(fl) H(fl) satisfying with & 0 on 0fl when m 2, where "Supported in Part by qNPq/Bril. MEIRA ">r By the way 0 fort>0, a cx as c (1.2)
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