Sign-changing and constant-sign solutions for elliptic problems involving nonlocal integro-differential operators

Superlinear elliptic problems with sign changing coefficients

Via variational methods, we study multiplicity of solutions for the problem    −∆u = λb(x)|u|q−2u + a u + g(x, u) in Ω , u = 0 on ∂Ω . where a simple example for g(x, u) is |u|p−2u; here a, λ are real parameters, 1 < q < 2 < p ≤ 2∗ and b(x) is a function in a suitable space L. We obtain a class of sign changing coefficients b(x) for which two non-negative solutions exist for any λ > 0, and a...

Multiplicity of positive solutions for fractional elliptic systems involving sign-changing weight

In this paper, we study the multiplicity results of positive solutions for a fractional elliptic system involving both concave-convex and critical growth terms. With the help of Morse theory and the Ljusternik-Schnirelmann category, we investigate how the coefficient h(x) of the critical nonlinearity affects the number of positive solutions of that problem and we get some results as regards the...

Least energy sign-changing solutions for a class of nonlocal Kirchhoff-type problems

In this paper, we consider the existence of least energy sign-changing solutions for a class of Kirchhoff-type problem [Formula: see text]where [Formula: see text] is a bounded domain in [Formula: see text], [Formula: see text], with a smooth boundary [Formula: see text], [Formula: see text] and [Formula: see text]. By using variational approach and some subtle analytical skills, the existence ...

Mountain pass and linking type sign-changing solutions for nonlinear problems involving the fractional Laplacian

where ⊂Rn (n≥ 2) is a bounded smooth domain, s ∈ (0, 1), (– )s denotes the fractional Laplacian, λ is a real parameter, the nonlinear term f satisfies superlinear and subcritical growth conditions at zero and at infinity. When λ≤ 0, we prove the existence of a positive solution, a negative solution and a sign-changing solution by combing minimax method with invariant sets of descending flow. Wh...

Multiple Solutions and a Sign-Changing Solution for Semi-Linear Elliptic Problems with Resonance