Sign-changing solutions for a class of p-Laplacian Kirchhoff-type problem with logarithmic nonlinearity

Abstract

"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 ≤ 2p < q < p* and N > p. 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."

Keywords

• p-laplacian kirchhoff-type equation
• nonlocal term
• variation methods
• sign-changing solutions