Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: an Orlicz-Sobolev space setting

We study the boundary value problem −div(log(1 + |∇u|)|∇u|∇u) = f(u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in R with smooth boundary. We distinguish the cases where either f(u) = −λ|u|u+|u|u or f(u) = λ|u|u−|u|u, with p, q > 1 , p+q < min{N, r}, and r < (Np−N+p)/(N−p). In the first case we show the existence of infinitely many weak solutions for any λ > 0. In the second case we prove t...

Some existence results on periodic solutions of Euler–Lagrange equations in an Orlicz–Sobolev space setting

In this paper we consider the problem of finding periodic solutions of certain Euler-Lagrange equations. We employ the direct method of the calculus of variations, i.e. we obtain solutions minimizing certain functional I. We give conditions which ensure that I is finitely defined and differentiable on certain subsets of Orlicz-Sobolev spaces W L associated to an N -function Φ. We show that, in ...

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.