Harnack's inequality for quasilinear elliptic equations with generalized Orlicz growth

An Orlicz-sobolev Space Setting for Quasilinear Elliptic Problems

In this paper we give two existence theorems for a class of elliptic problems in an Orlicz-Sobolev space setting concerning both the sublinear and the superlinear case with Neumann boundary conditions. We use the classical critical point theory with the Cerami (PS)-condition.

Anisotropic quasilinear elliptic equations with variable exponent

We study some anisotropic boundary value problems involving variable exponent growth conditions and we establish the existence and multiplicity of weak solutions by using as main argument critical point theory. 2000 Mathematics Subject Classification: 35J60, 35J62, 35J70.

Quasilinear Elliptic Equations with Critical Exponents

has no solution if Ω ⊂ R , N ≥ 3, is bounded and starshaped with respect to some point, and 2∗ = 2N/(N − 2). In (P0) the nonlinear term is a power of u with the critical exponent (N + 2)/(N − 2). This terminology comes from the fact that the continuous Sobolev imbeddings H 0 (Ω) ⊂ L(Ω), for p ≤ 2∗ and Ω bounded, are also compact except when p = 2∗. This loss of compactness reflects in that the ...

Large Solutions for Quasilinear Elliptic Equations

Quasilinear Elliptic Problems with Nonstandard Growth

We prove the existence of solutions to Dirichlet problems associated with the p(x)-quasilinear elliptic equation Au = − div a(x, u,∇u) = f(x, u,∇u). These solutions are obtained in Sobolev spaces with variable exponents.