Asymptotics for quasilinear elliptic non-positone problems

On Multiple Positive Solutions of Positone and Non-positone Problems

In this paper, we consider the following problem: − u= f (u) in , u= 0 on ∂ , (1.1) where is the ball BR = {x ∈ R ; |x| < R}, | · | is the Euclidean norm in R, and f : R+ → R is a locally Lipschitzian continuous function. We are concerned with two classes of problems, namely, (i) the positone problem: f (0)≥ 0; (ii) the non-positone problem: f (0) < 0. The study of positone problems was initiat...

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.

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.

An Approach to Quasilinear Elliptic Problems

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.