Existence of ground states for a Kirchhoff type problem without 4-superlinear condition期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Existence of ground states for a Kirchhoff type problem without 4-superlinear condition

Authors:	Ke Wu

Affiliation:	Department of Mathematics, Yunnan Normal University, Kunming, Yunnan 650500, PR China

Abstract:	We consider the existence of ground state solutions for the Kirchhoff type problem $\{\begin{matrix} ? (a + b \int_{R^{N}} {\| ? u \|}^{2} d x) △ u + V (x) u = {\| u \|}^{p ? 2} u, & x \in R^{N}, \\ u \in H^{1} (R^{N}), \end{matrix} is=$ where $a, b > 0$ , $N = 1, 2, 3$ and $2 < p < 2^{1}$ . Here we are interested in the case that $2 < p \leq 4$ since the existence of ground state for $4 < p \leq 2^{1}$ is easily obtained by a standard variational argument. Our method is based on a Poho $\overset{?}{z}$ aev type identity.

Keywords:	4-sublinear problem Kirchhoff equation
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