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EXISTENCE AND CONCENTRATION RESULTS FOR KIRCHHOFF-TYPE SCHR¨O DINGER SYSTEMS WITH STEEP POTENTIAL WELL

Dengfeng Lu
대한수학회 (The Korean Mathematical Society)|2015.03|대한수학회보 (Bulletin of the KMS)|제52권 제2호|pp. 661-677

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키워드

concentrationvariational methodKirchhoff-type Schr¨odinger systemsteep potential well
주제분류수학

초록

In this paper, we consider the following Kirchhoff-type Schr¨odinger system −(a1 + b1 ∫R3 |∇u|2dx)△u + γV (x)u = 2α/α+β|u|α−2u|v|β in R3, −(a2 + b2 ∫R3 |∇u|2dx)△u + γV (x)u = 2β/α+β|u|α|v|β−2v in R3, u, v ∈ H1(R3), where ai and bi are positive constants for i = 1, 2, γ > 0 is a parameter, V (x) and W(x) are nonnegative continuous potential functions. By applying the Nehari manifold method and the concentration-compactness principle, we obtain the existence and concentration of ground state solutions when the parameter γ is sufficiently large.

Abstract

In this paper, we consider the following Kirchhoff-type Schr¨odinger system −(a1 + b1 ∫R3 |∇u|2dx)△u + γV (x)u = 2α/α+β|u|α−2u|v|β in R3, −(a2 + b2 ∫R3 |∇u|2dx)△u + γV (x)u = 2β/α+β|u|α|v|β−2v in R3, u, v ∈ H1(R3), where ai and bi are positive constants for i = 1, 2, γ > 0 is a parameter, V (x) and W(x) are nonnegative continuous potential functions. By applying the Nehari manifold method and the concentration-compactness principle, we obtain the existence and concentration of ground state solutions when the parameter γ is sufficiently large.

참고문헌 (20)

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