Limit Property of an L2-Normalized Solution for an L2-Subcritical Kirchhoff-Type Equation with a Variable Exponent

Abstract

This paper is concerned with the following L2-subcritical Kirchhoff-type equation −a+b∫R2|∇u|2dxsΔu+V(x)u=μu+β|u|2u,x∈R2, with ∫R2|u|2dx=1. We give a detailed analysis of the limit property of the L2-normalized solution when exponent s tends toward 0 from the right (i.e., s↘0). Our research extends previous works, in which the authors have displayed the limit behavior of L2-normalized solutions when s=1 as a↘0 or b↘0.