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- W2083144411 abstract "Abstract In this paper, we will study the existence and qualitative property of standing waves ψ ( x , t ) = e − i E t e u ( x ) for the nonlinear Schrodinger equation i e ∂ ψ ∂ t + e 2 2 m Δ x ψ − ( V ( x ) + E ) ψ + K ( x ) | ψ | p − 1 ψ = 0 , ( t , x ) ∈ R + × R N . Let G ( x ) = [ V ( x ) ] p + 1 p − 1 − N 2 [ K ( x ) ] − 2 p − 1 and suppose that G ( x ) has k local minimum points. Then, for any l ∈ { 1 , … , k } , we prove the existence of the standing waves in H 1 ( R N ) having exactly l local maximum points which concentrate near l local minimum points of G ( x ) respectively as e → 0 . The potentials V ( x ) and K ( x ) are allowed to be either compactly supported or unbounded at infinity. Therefore, we give a positive answer to a problem proposed by Ambrosetti and Malchiodi (2007) [2] ." @default.
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- W2083144411 date "2010-10-01" @default.
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- W2083144411 title "Multi-peak bound states for Schrödinger equations with compactly supported or unbounded potentials" @default.
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- W2083144411 doi "https://doi.org/10.1016/j.anihpc.2010.05.003" @default.
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