Multiplicity results for the non-homogeneous fractional p -Kirchhoff equations with concave–convex 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 results for hybrid fractional differential equations with Hilfer fractional derivative

This paper investigates the solvability, existence and uniqueness of solutions for a class of nonlinear fractional hybrid differential equations with Hilfer fractional derivative in a weighted normed space. The main result is proved by means of a fixed point theorem due to Dhage. An example to illustrate the results is included.

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

Fibered nonlinearities for p(x)-Laplace equations

The purpose of this paper is to give some geometric results on the following problem: −div ( α(x)|∇u(X)|p(x)−2∇u(X) ) = f(x, u(X)) in Ω, (1.1) where f = f(x, u) ∈ L∞(Rm×R) is differentiable in u with fu ∈ L∞(R), α ∈ L∞(Rm), with inf Rm α > 0, p ∈ L∞(Rm), with p(x) ≥ 2 for any x ∈ R, and Ω is an open subset of R. Here, u = u(X), with X = (x, y) ∈ R × Rn−m. As well known, the operator in (1.1) co...