Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2017; 54(3): 1023-1036

Online first article January 4, 2017      Printed May 31, 2017

https://doi.org/10.4134/BKMS.b160467

Copyright © The Korean Mathematical Society.

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

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