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http://dx.doi.org/10.4134/BKMS.b160467

POSITIVE SOLUTIONS TO p-KIRCHHOFF-TYPE ELLIPTIC EQUATION WITH GENERAL SUBCRITICAL GROWTH  

Zhang, Huixing (Department of Mathematics China University of Mining and Technology)
Zhang, Ran (Department of Mathematics China University of Mining and Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.3, 2017 , pp. 1023-1036 More about this Journal
Abstract
In this paper, we study the existence of positive solutions to the p-Kirchhoff elliptic equation involving general subcritical growth $(a+{\lambda}{\int_{\mathbb{R}^N}{\mid}{\nabla}u{\mid}^pdx+{\lambda}b{\int_{\mathbb{R}^N}{\mid}u{\mid}^pdx)(-{\Delta}_pu+b{\mid}u{\mid}^{p-2}u)=h(u)$, 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;
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