Existence of Positive Solution for Kirchhoff Problems.

In this work, we study the following Kirchhoff type problem -(a+b∫Ω|∇u|pdx)Δpu=g(x)u-γ+λf(x,u),inΩ,u=0,on∂Ω,where p≥2, Ω is a regular bounded domain in RN, (N≥3). Firstly, for p>2, 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 λ=0 we prove an uniqueness result. We use the variational method to prove our main results. [ABSTRACT FROM AUTHOR]