Existence of nontrivial solutions for Schrödinger‐Kirchhoff type equations with critical or supercritical growth

Abstract

In this paper, we study the following Schrödinger‐Kirchhoff–type equation with critical or supercritical growth urn:x-wiley:mma:media:mma4652:mma4652-math-0001 where a>0, b>0, λ>0, and p≥6. Under some suitable conditions, we prove that the equation has a nontrivial solution for small λ>0 by variational method. Moreover, we regard b as a parameter and obtain a convergence property of the nontrivial solution as b↘0. Our main contribution is related to the fact that we are able to deal with the case p>6.