Article ID Journal Published Year Pages File Type
4611680 Journal of Differential Equations 2012 22 Pages PDF
Abstract

We study the existence, multiplicity and concentration behavior of positive solutions for the nonlinear Kirchhoff type problem{−(ε2a+εb∫R3|∇u|2)Δu+V(x)u=f(u)in R3,u∈H1(R3),u>0in R3, where ε>0ε>0 is a parameter and a,b>0a,b>0 are constants; V is a positive continuous potential satisfying some conditions and f is a subcritical nonlinear term. We relate the number of solutions with the topology of the set where V attains its minimum. The results are proved by using the variational methods.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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