One solution for nonlocal fourth order equations

A critical point result for differentiable functionals is exploited in order to prove that a suitable class of fourth-order boundary value problem of Kirchhoff-type possesses at least one weak solution under an asymptotical behavior of the nonlinear datum at zero. Some examples to illustrate the results are given.

Blow-up and energy decay for a class of wave equations with nonlocal Kirchhoff-type diffusion and weak damping

The purpose of this paper is to study the following equation driven by a nonlocal integro-differential operator $\mathcal{L}_K$: \[u_{tt}+[u]_s^{2(\theta-1)}\mathcal{L}_Ku+a|u_t|^{m-1}u_t=b|u|^{p-1}u\] with homogeneous Dirichlet boundary condition and initial data, where $[u]^2_s$ is the Gagliardo seminorm, $a\geq 0,~b>0,~0

Existence and Multiplicity of Solutions for a Biharmonic Equation with p(x)-Kirchhoff Type

Based on the basic theory and critical point theory of variable exponential Lebesgue Sobolev space, this paper investigates the existence and multiplicity of solutions for a class of nonlocal elliptic equations with Navier boundary value conditions when (AR) condition does not hold and improves or generalizes the original conclusions.