Existence of Positive Solution for Kirchhoff Problems

摘要

In this work, we study the following Kirchhoff type problem where p2, is a regular bounded domain in RN, (N3). Firstly, for p2, we prove under some appropriate conditions on the singularity and the nonlinearity the existence of nontrivial weak solution to this problem. For p=2, we show, under supplementary condition, the positivity of this solution. Moreover, in the case =0 we prove an uniqueness result. We use the variational method to prove our main results.