Existence of multiple nontrivial solutions for a $p$-Kirchhoff typeelliptic problem involving sign-changing weight functions

Yuanxiao  Li; Ming Mei; Kaijun Zhang

doi:10.3934/dcdsb.2016.21.883

Article Contents

2016, Volume 21, Issue 3: 883-908. Doi: 10.3934/dcdsb.2016.21.883

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Existence of multiple nontrivial solutions for a $p$-Kirchhoff type elliptic problem involving sign-changing weight functions

1.
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024
2.
Department of Mathematics, Champlain College Saint-Lambert, Quebec, J4P 3P2
3.
School of Mathematics and Statistics, Northeast Normal University, Changchun, MO 130024

Received: March 31, 2015

Revised: November 30, 2015

Published: April 2016

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Abstract

This paper deals with a $p$-Kirchhoff type problem involving sign-changing weight functions. It is shown that under certain conditions, by means of variational methods, the existence of multiple nontrivial nonnegative solutions for the problem with the subcritical exponent are obtained. Moreover, in the case of critical exponent, we establish the existence of the solutions and prove that the elliptic equation possesses at least one nontrivial nonnegative solution.

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Mathematics Subject Classification: 35D30, 35J20, 35J62.

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References

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