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.
Huixing Zhang and Ran Zhang
China University of Mining and Technology, China University of Mining and Technology
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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