On existence and multiplicity of solutions for Kirchhoff-type equations with a nonsmooth potential

Existence and multiplicity of solutions for a Neumann-type p(x)-Laplacian equation with nonsmooth potential

In this paper we study Neumann-type p(x)-Laplacian equation with nonsmooth potential. Firstly, applying a version of the non-smooth three-critical-points theorem we obtain the existence of three solutions of the problem in W (Ω). Finally, we obtain the existence of at least two nontrivial solutions, when α− > p.

Existence and multiplicity of positive solutions for a class of p(x)-Kirchhoff type equations

* Correspondence: [email protected] Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China Abstract In this article, we study the existence and multiplicity of positive solutions for the Neumann boundary value problems involving the p(x)-Kirchhoff of the form ⎪⎨⎪⎩ −M (∫ 1 p(x) (|∇u|p(x) + λ|u|p(x))dx ) (div (|∇u|p(x)−2∇u) − λ|u|p(x)−2u) = f (x, u) in , ∂u ∂v = 0...

Existence and multiplicity of positive solutions for a coupled system of perturbed nonlinear fractional differential equations

In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.

Existence and concentration of solutions for the nonlinear Kirchhoff type equations with steep well potential

Existence and multiplicity of solutions for a class of fractional Kirchhoff-type problem∗

In this paper, we establish the existence and multiplicity of solutions to the following fractional Kirchhoff-type problem M(∥u∥)(−∆)u = f(x, u(x)), in Ω u = 0 in R\Ω, where N > 2s with s ∈ (0, 1), Ω is an open bounded subset of R with Lipschitz boundary, M and f are two continuous functions, and (−∆) is a fractional Laplace operator. Our main tools are based on critical point theorems and the ...