Existence of multiple nontrivial solutions for a $p$-Kirchhoff typeelliptic problem involving sign-changing weight functions
2016
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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