This paper is devoted to the following p-Kirchhoff type of problems:

$$\begin{aligned} \left\{ \begin{array}{ll} -(a+b\int _{\Omega }|\nabla u|^{p}\,\text{ d }x)\Delta _{p} u=-\lambda |u|^{q-2}u+f(x,u),x\in \Omega \\ u=0,x\in \partial \Omega . \end{array} \right. \end{aligned}$$

Without assuming the standard subcritical polynomial growth condition ensuring the compactness of a bounded (P.S.) sequence, we show that the Dirichlet boundary value problem has at least a weak nontrivial solution by using Morse theory.

中文翻译：

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基于莫尔斯理论的一类p -Kirchhoff方程解的存在性

本文致力于以下p -Kirchhoff类型的问题：

$$ \ begin {aligned} \ left \ {\ begin {array} {ll}-（a + b \ int _ {\ Omega} | \ nabla u | ^ {p} \，\ text {d} x）\ Delta _ {p} u =-\ lambda | u | ^ {q-2} u + f（x，u），x \在\ Omega \\ u = 0，x \在\ partial \ Omega中。\ end {array} \ right。\ end {aligned} $$

在不假设标准亚临界多项式增长条件确保有界（PS）序列紧凑的情况下，我们使用莫尔斯理论证明Dirichlet边值问题至少具有弱非平凡解。