Abstract
We study the existence, multiplicity and concentration behavior of positive solutions for the nonlinear Kirchhoff type problem { − ( ε 2 a + ε b ∫ R 3 | ∇ u | 2 ) Δ u + V ( x ) u = f ( u ) in R 3 , u ∈ H 1 ( R 3 ) , u > 0 in R 3 , where ε > 0 is a parameter and a , 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.
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