An approach to quasilinear elliptic problems

An Approach to Quasilinear Elliptic Problems

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.

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.

Landesman-Laser Conditions and Quasilinear Elliptic Problems

In this paper we consider two elliptic problems. The first one is a Dirichlet problem while the second is Neumann. We extend all the known results concerning Landesman-Laser conditions by using the Mountain-Pass theorem with the Cerami (PS) condition.

A note on quasilinear elliptic eigenvalue problems

We study an eigenvalue problem by a non-smooth critical point theory. Under general assumptions, we prove the existence of at least one solution as a minimum of a constrained energy functional. We apply some results on critical point theory with symmetry to provide a multiplicity result.