Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms

Yanheng Ding, Cheng Lee

Research output: Contribution to journalArticle

69 Citations (Scopus)

Abstract

Based on new information concerning strongly indefinite functionals without Palais-Smale conditions, we study existence and multiplicity of solutions of the Schrödinger equation { -Δu + V(x)u = g(x,u) for x ε ℝN, u(x) → 0 as x → ∞, where V and g are periodic with r espect to x and 0 lies in a gap of σ(-Δ+V). Supposing g is asymptotically linear as u → ∞ and symmetric in u, we obtain infinitely many geometrically distinct solutions. We also consider the situation where g is super linear with mild assumptions different from those studied previously, and establish the existence and multiplicity.

Original languageEnglish
Pages (from-to)137-163
Number of pages27
JournalJournal of Differential Equations
Volume222
Issue number1
DOIs
Publication statusPublished - 2006 Mar 1

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Palais-Smale Condition
Asymptotically Linear
Multiplicity of Solutions
Multiple Solutions
Existence of Solutions
Multiplicity
Distinct
Term

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

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abstract = "Based on new information concerning strongly indefinite functionals without Palais-Smale conditions, we study existence and multiplicity of solutions of the Schr{\"o}dinger equation { -Δu + V(x)u = g(x,u) for x ε ℝN, u(x) → 0 as x → ∞, where V and g are periodic with r espect to x and 0 lies in a gap of σ(-Δ+V). Supposing g is asymptotically linear as u → ∞ and symmetric in u, we obtain infinitely many geometrically distinct solutions. We also consider the situation where g is super linear with mild assumptions different from those studied previously, and establish the existence and multiplicity.",
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Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms. / Ding, Yanheng; Lee, Cheng.

In: Journal of Differential Equations, Vol. 222, No. 1, 01.03.2006, p. 137-163.

Research output: Contribution to journalArticle

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