Positive solutions to Schrödinger-Kirchhoff equations with inverse potential.

This paper is concerned with the existence of positive solutions to Schrödinger-Kirchhoff-type equations (P) − a + b ∫ R 3 | ∇ u | 2 Δ u + V (x) u = | u | p − 1 u i n R 3 , u ∈ H 1 ( R 3) , where a and b are two positive constants, p ∈ (1 , 5) and V : R 3 → R is a potential function. Under certain assumptions on V, we prove that (P) has no ground state solution. However, we can show (P) has a positive bound state solution by applying a new version of the global compactness lemma and the linking theorem. [ABSTRACT FROM AUTHOR]