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Positive solutions to p-Kirchhoff-type elliptic equation with general subcritical growth

Huixing Zhang|Ran Zhang
대한수학회 (The Korean Mathematical Society)|2017.05|대한수학회보 (Bulletin of the KMS)|제54권 제3호|pp. 1023-1036

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키워드

$p$-Kirchhoff-type equationsubcritical growthasymptotics
주제분류수학

초록

In this paper, we study the existence of positive solutions to the $p$-Kirchhoff elliptic equation involving general subcritical growth $$ (a+\lambda\int_{\mathbb{R}^N}|\nabla u|^p dx+\lambda b\int_{\mathbb{R}^N}|u|^p dx)(-\Delta_p u+b|u|^{p-2}u)=h(u),\ \mbox{in}\ \mathbb{R}^N, $$ where $a,\ b>0$, ${\lambda}$ is a parameter and the nonlinearity $h(s)$ satisfies the weaker conditions than the ones in our known literature. We also consider the asymptotics of solutions with respect to the parameter $\lambda$.

Abstract

In this paper, we study the existence of positive solutions to the $p$-Kirchhoff elliptic equation involving general subcritical growth $$ (a+\lambda\int_{\mathbb{R}^N}|\nabla u|^p dx+\lambda b\int_{\mathbb{R}^N}|u|^p dx)(-\Delta_p u+b|u|^{p-2}u)=h(u),\ \mbox{in}\ \mathbb{R}^N, $$ where $a,\ b>0$, ${\lambda}$ is a parameter and the nonlinearity $h(s)$ satisfies the weaker conditions than the ones in our known literature. We also consider the asymptotics of solutions with respect to the parameter $\lambda$.

참고문헌 (21)

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