Ground state sign-changing solutions for semilinear Dirichlet problems

On the Existence of Sign Changing Solutions for Semilinear Dirichlet Problems

where Ω ⊂ R is a bounded domain with Lipschitz boundary and f : R → R is of class C with f(0) = 0. Thus u0 ≡ 0 is a trivial solution of (D) and we are interested in finding and studying nontrivial solutions. One way of obtaining these is to compare the behavior of f near the origin and near infinity. We shall always assume that f grows subcritically at infinity so that variational methods can b...

Multiple Sign-changing Solutions for Kirchhoff Type Problems

This article concerns the existence of sign-changing solutions to nonlocal Kirchhoff type problems of the form

Infinitely Many Solutions for a Semilinear Elliptic Equation with Sign-Changing Potential

Multiple Solutions for Semilinear Elliptic Equations with Sign-changing Potential and Nonlinearity

In this article, we study the multiplicity of solutions for the semilinear elliptic equation −∆u + a(x)u = f(x, u), x ∈ Ω, u = 0, x ∈ ∂Ω, where Ω ⊂ RN (N ≥ 3), the potential a(x) satisfies suitable integrability conditions, and the primitive of the nonlinearity f is of super-quadratic growth near infinity and is allowed to change sign. Our super-quadratic conditions are weaker the usual super-q...

Multiple Positive Solutions for Semilinear Elliptic Equations with Sign - Changing Weight Functions

and Applied Analysis 3 In order to describe our main result, we need to define Λ0 ( 2 − q ( p − q‖a‖L∞ ) 2−q / p−2 ( p − 2 ( p − q)‖b ‖Lq∗ ) S p 2−q /2 p−2 q/2 p > 0, 1.3 where ‖a‖L∞ supx∈RNa x , ‖b ‖Lq∗ ∫ RN |b x |qdx 1/q∗ and Sp is the best Sobolev constant for the imbedding of H1 R into L R . Theorem 1.1. Assume that a1 , b1 b2 hold. If λ ∈ 0, q/2 Λ0 , Ea,λb admits at least two positive solu...