This paper deals with a p-Kirchhoff type problem involving signchanging weight functions. It is shown that under certain conditions, by means of variational methods, the existence of multiple nontrivial nonnegative solutions for the problem with the subcritical exponent are obtained. Moreover, in the case of critical exponent, we establish the existence of the solutions and prove that the ellip...

This paper deals with the existence and multiplicity of solutions for a perturbed nonlocal fourth-order class p(·)&q(·)-Kirchhoff elliptic systems under Navier boundary conditions. By using variational method Ricceri’s critical point theorem, we can find proper conditions to ensure that (p(x),q(x))-Kirchhoff has at least three weak solutions. We have extended improved some recent results. T...

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.

The present paper deals with a Kirchhoff problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain Ω of R^{N}. The problem studied is a stationary version of the orig inal Kirchhoff equation, involving the p(x)-Lap lacian operator, in the framework of the variable exponent Lebesgue and Sobolev spaces. The question of the existence of weak solutions is treated. Appl...

We consider the existence and uniqueness of solution to a fourth-order Kirchhoff type elliptic equation with strong singularity. By using Ekeland’s variational principle in suitable subsets $H_0^2(\Omega )$, we obtain necessary sufficient conditi

This paper deals with the existence and multiplicity of solutions for a class Kirchhoff type elliptic systems involving nonlinearities Trudinger-Moser exponential growth. We first study following system: $$\begin{aligned} \left\{ \begin{array}{ll} -\big (a_1+b_1\Vert u\Vert ^{2(\theta _1-1)}\big )\Delta u= \lambda H_u(x,u,v) &{} \quad \text{ in }\ \ \Omega ,\\ (a_2+b_2\Vert v\Vert _2-1)}\big v=...