CPAA
Multiple nontrivial solutions to a $p$-Kirchhoff equation
Anran Li Jiabao Su
In this paper, by computing the relevant critical groups, we obtain nontrivial solutions via Morse theory to the nonlocal $p$-Kirchhoff-type quasilinear elliptic equation \begin{eqnarray} (P)\quad\quad &&\displaystyle\bigg[M\bigg(\int_\Omega|\nabla u|^p dx\bigg)\bigg]^{p-1}(-\Delta_pu) = f(x,u), \quad x\in\Omega,\\ && u=0, \quad x\in \partial \Omega, \end{eqnarray} where $\Omega \subset \mathbb R^N$ is a bounded open domain with smooth boundary $\partial \Omega$ and $N \geq 3$.
keywords: critical point local linking. Nonlocal p-Kirchhoff problem Morse theory critical group

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