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Advanced Nonlinear Studies

Editor-in-Chief: Ahmad, Shair

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Volume 19, Issue 3


An Abstract Linking Theorem Applied to Indefinite Problems Via Spectral Properties

Liliane A. Maia / Mayra Soares
Published Online: 2019-03-08 | DOI: https://doi.org/10.1515/ans-2019-2041


An abstract linking result for Cerami sequences is proved without the Cerami condition. It is applied directly in order to prove the existence of critical points for a class of indefinite problems in infinite-dimensional Hilbert Spaces. The applications are given to Schrödinger equations. Here spectral properties inherited by the potential features are exploited in order to establish a linking structure, and hence hypotheses of monotonicity on the nonlinearities are discarded.

Keywords: Linking Structure; Variational Methods; Spectral Theory; Schrödinger Equation; Asymptotically Linear

MSC 2010: 35J10; 35J20; 35J60; 35P05


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About the article

Received: 2018-11-05

Revised: 2019-02-09

Accepted: 2019-02-11

Published Online: 2019-03-08

Published in Print: 2019-08-01

Funding Source: Conselho Nacional de Desenvolvimento Científico e Tecnológico

Award identifier / Grant number: 308378/2017-2

Funding Source: Fundação de Apoio à Pesquisa do Distrito Federal

Award identifier / Grant number: 0193.001300/2016

Research supported by FAPDF 0193.001300/2016, CNPq/PQ 308378/2017-2 (Brazil).

Citation Information: Advanced Nonlinear Studies, Volume 19, Issue 3, Pages 545–567, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2019-2041.

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