Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2016.06.03
  • Published : 2017.05.31
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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 ${\lambda}$.

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References

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