Existence and Limit Behavior of Constraint Minimizers for a Varying Non-Local Kirchhoff-Type Energy Functional

Abstract

In this paper, we study the constrained minimization problem for an energy functional which is related to a Kirchhoff-type equation. For s=1, there many articles have analyzed the limit behavior of minimizers when η>0 as b→0+ or b>0 as η→0+. When the equation involves a varying non-local term ∫R3|∇u|2dxs, we give a detailed limit behavior analysis of constrained minimizers for any positive sequence {ηk} with ηk→0+. The present paper obtains an interesting result on this topic and enriches the conclusions of previous works.