Multiplicity results for a class ofp(x)-Kirchhoff type equations with combined nonlinearities

MULTIPLICITY RESULTS FOR A CLASS OF p(x)-KIRCHHOFF TYPE EQUATIONS WITH COMBINED NONLINEARITIES

Using the mountain pass theorem combined with the Ekeland variational principle, we obtain at least two distinct, non-trivial weak solutions for a class of p(x)-Kirchhoff type equations with combined nonlinearities. We also show that the similar results can be obtained in the case when the domain has cylindrical symmetry.

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...

Multiplicity Results for Perturbed Fourth-order Kirchhoff-type Problems

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 ...

On a class of Kirchhoff type systems with nonlinear boundary condition

A class of Kirchhoff type systems with nonlinear boundary conditions considered in this paper. By using the method of Nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.