THE EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF INDEFINITE WEIGHT SEMILINEAR ELLIPTIC PROBLEMS WITH CRITICAL SOBOLEV EXPONENT

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.

Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Existence of Positive Solutions for Semilinear Elliptic Systems with Indefinite Weight

This article concerns the existence of positive solutions of semilinear elliptic system −∆u = λa(x)f(v), in Ω, −∆v = λb(x)g(u), in Ω, u = 0 = v, on ∂Ω, where Ω ⊆ RN (N ≥ 1) is a bounded domain with a smooth boundary ∂Ω and λ is a positive parameter. a, b : Ω → R are sign-changing functions. f, g : [0,∞) → R are continuous with f(0) > 0, g(0) > 0. By applying LeraySchauder fixed point theorem, w...

Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.