Solutions of homogeneous fractional p-Kirchhoff equations in R^N

$L^p$-existence of mild solutions of fractional differential equations in Banach space

We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work. 

Periodic solutions of forced Kirchhoff equations

We consider Kirchhoff equations for vibrating strings and elastic membranes under the action of an external forcing of period 2π/ω and small amplitude ε. We prove existence, regularity and local uniqueness of 2π/ω-periodic solutions of order ε by means of a Nash-Moser iteration scheme; the results hold for parameters (ω, ε) in a Cantor-like set which has asymptotically full measure for ε→ 0.

Multiple Solutions of Quasilinear Elliptic Equations in RN

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...

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces