Positive solutions to $p$-Kirchhoff-type elliptic equation with general subcritical growth
Bull. Korean Math. Soc. 2017 Vol. 54, No. 3, 1023-1036
Published online January 4, 2017
Printed May 31, 2017
Huixing Zhang and Ran Zhang
China University of Mining and Technology, China University of Mining and Technology
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 $\lambda$.
Keywords : $p$-Kirchhoff-type equation, subcritical growth, asymptotics
MSC numbers : 35J20, 35J15, 35J60
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