带变号非线性项的p-Kirchhoff型问题的多解性（英文）

Existence of Multiple Solutions for a p-Kirchhoff Problem With Sign-changing Nonlinearity

本文主要研究带有零Dirichlet边界条件的p-Kirchhoff型方程(α+λ((∫_Ω(|▽u|~p+V(x)|u|~p)dx)~T)(-△_pu+V(x)|u|^(p-2)u)=f(x,u),x∈Ω解的存在性与多解性,其中Ω是R^N(N≥3)中的有界光滑区域,a,λ>0,τ>0,函数V.f连续且满足一定的条件.利用变分法,得到了该问题无穷多个非平凡解的存在性.

In this paper, we study the multiplicity of solutions for the following p-Kirchhoff equation with zero Dirichlet boundary condition, where ~ is a bounded domain with smooth boundary in RN （N ≥ 3）, a, λ〉 0, τ〉 0, and V, f are continuous functions satisfying some conditions. By using the variational method, we get the existence of infinitely many nontrivial solutions for the previous equation.