Multi-bump Bound States of Schrödinger Equations with a Critical Frequency

Author： Cao Daomin  

Publisher： Springer Publishing Company

ISSN： 0025-5831

Source： Mathematische Annalen, Vol.336, Iss.4, 2006-12, pp. : 925-948

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Abstract

We consider existence and qualitative properties of standing wave solutions to the nonlinear Schrödinger equation with E being a critical frequency in the sense that inf . We verify that if the zero set of W − E has several isolated points x i ( ) near which W − E is almost exponentially flat with approximately the same behavior, then for h > 0 small enough, there exists, for any integer k, , a standing wave solution which concentrates simultaneously on , where is any given subset of . This generalizes the result of Byeon and Wang in 3 (Arch Rat Mech Anal 165: 295–316, 2002).

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