Harnack inequality and continuity of solutions for quasilinear elliptic equations in Sobolev spaces with variable exponent

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.

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.

Entire solutions of multivalued nonlinear Schrodinger equations in Sobolev spaces with variable exponent

We establish the existence of an entire solution for a class of stationary Schrödinger equations with subcritical discontinuous nonlinearity and lower bounded potential that blows-up at infinity. The abstract framework is related to Lebesgue–Sobolev spaces with variable exponent. The proof is based on the critical point theory in the sense of Clarke and we apply Chang’s version of the Mountain ...

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition

‎Some functional inequalities‎ ‎in variable exponent Lebesgue spaces are presented‎. ‎The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non‎- ‎increasing function which is‎‎$$‎‎int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleq‎‎Cint_0^infty f(x)^{p(x)}u(x)dx‎,‎$$‎ ‎is studied‎. ‎We show that the exponent $p(.)$ for which these modular ine...