Construction of high‐energy solutions for the supercritical biharmonic Schrödinger equation

Abstract

We consider the problem Δ 2 u = V(x)u p + in R N with u, Δu → 0 as |x| → + ∞, where p = N+4 N−4 , N ≥ 5, V is a positive continuous potential. Our aim is to construct high-energy solutions for this equation by applying the finite-dimensional reduction method and the penalization method. KEYWORDSbiharmonic equation, reduction method, supercriticalWhen > 0 is small, they established the relationship between the number of solutions and the profile of V, h, g. Also, without the restriction on , they obtained a multiplicity result.Recently, Guo, Tan, and Wang 7 concerned with the existence of least energy solutions for the following biharmonic equations:How to cite this article: Gan L. Construction of high-energy solutions for the supercritical biharmonic Schrödinger equation. Math Meth Appl Sci. 2019;42:883-891. https://doi.