Multiple sign-changing solutions for nonlinear fractional Kirchhoff equations

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

Multiple Positive Solutions for Nonlinear Semipositone Fractional Differential Equations

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...

Solutions for a nonlinear fractional boundary value problem with sign-changing Green’s function

This paper considers the existence, uniqueness and non-existence of solution for a quasi-linear fractional boundary value problems with sign-changing Green’s function. Under certain growth conditions on the nonlinear term, we employ the Leray-Schauder alternative fixed point theorem to obtain an existence result of nontrivial solution and use the Banach contraction mapping principle to obtain a...

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces