Concentrating solutions for a biharmonic problem with supercritical growth - Liu, Zhongyuan (Topological Methods in Nonlinear Analysis, 2023)
In this paper we consider the following supercritical biharmonic problem: cases Δ^2 u= K(x)u^p+ε&in Ω, u> 0 &in Ω, u=Δ u=0&on Ω, cases where K(x)C^3(Ω) is a nonnegative function, p=(N+4)/(N-4), ε> 0, Ω is a smooth bounded domain in R^N, N≥6. We show that, for ε small enough, there exists a family of concentrating solutions under certain assumptions on the critical points of the function K(x).