| Summary: | "In this paper, we study the existence of ground state sign-changing solutions for following $p$-Laplacian Kirchhoff-type problem with logarithmic nonlinearity\begin{equation*} \left\{ \renewcommand{\arraystretch}{1.25} \begin{array}{ll} -(a+ b\int _{\Omega}|\nabla u|^{p}dx)\Delta_p u=|u|^{q-2}u\ln u^2, ~x\in\Omega \\ u=0, ~\ x\in \partial\Omega, \end{array} \right.\end{equation*}where $\Omega\subset \mathbb{R}^{N}$ is a smooth bounded domain, $a, b>0$ are constant, 4 ≤ 2<em>p</em> < <em>q</em> < <em>p</em><sup>*</sup> and <em>N</em> > <em>p</em>. By using constraint variational method, topological degree theory and the quantitative deformation lemma, we prove the existence of ground state sign-changing solutions with precisely two nodal domains."
|
|---|