Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in $R^3$
By Gongbao Li, Hongyu Ye. 2013
129 citations recorded by the source corpus.
In this paper, we study the following nonlinear problem of Kirchhoff type with pure power nonlinearities: (a+b\ds\int_{\R^3}|D u|^2\right)\Delta u+V(x)u=|u|^{p-1}u, u\in H^1(\R^3), u>0, $x\in \R^3, where $a,$ $b>0$ are constants, $2 0, $x\in \R^3$, where $\varepsilon>0$ is a parameter, $V(x)$ is a positive continuous potential and $f(u)\thicksim |u|^{p-1}u$ with $3<p<5$ and satisfies the Ambrosetti-Rabinowitz type condition. Our main results extend also the arguments used in [7,36], which deal with Schr\"{o}dinger-Poisson system with pure power nonlinearities, to the Kirchhoff type problem.
View Paper: https://www.semanticscholar.org/paper/fab923aeb1190f6a0c33ef151bb0727acb5f8e68
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Citations in the corpus
- Infinitely many sign-changing solutions for Kirchhoff type problems in R3 (2019, background): “1 in [13], we have the following Pohozaev type identity.”
- Ground State Solutions for the Nonlinear Schrödinger–Bopp–Podolsky System with Critical Sobolev Exponent (2020, unknown): “Following the idea of [18], let (un)n ⊂M∞μ be such that 0 < lim n→∞ I ∞ μ (un) = c∞ < 1 3 3 2 .”