Infinitely Many Solutions of the Neumann Problem for Elliptic systems in Anisotropic Variable Exponent Sobolev Spaces

Infinitely Many Periodic Solutions for Variable Exponent Systems

Existence of solutions for elliptic systems with critical Sobolev exponent ∗

We establish conditions for existence and for nonexistence of nontrivial solutions to an elliptic system of partial differential equations. This system is of gradient type and has a nonlinearity with critical growth.

Concentrating solutions for an anisotropic elliptic problem with large exponent

We consider the following anisotropic boundary value problem ∇(a(x)∇u) + a(x)u = 0, u > 0 in Ω, u = 0 on ∂Ω, where Ω ⊂ R2 is a bounded smooth domain, p is a large exponent and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of concentrating solutions. We show that at a given strict local maximum point of a(x), there exist arbitraril...

Entropy Solutions for Nonlinear Elliptic Anisotropic Homogeneous Neumann Problem

The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent

In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.