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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

GENERALIZED NEHARI MANIFOLD AND SEMILINEAR SCHRODINGER EQUATION WITH WEAK MONOTONICITY CONDITION ON THE NONLINEAR TERM

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Autor(es):
De Paiva, Francisco Odair ; Kryszewski, Wojciech ; Szulkin, Andrzej
Número total de Autores: 3
Tipo de documento: Artigo Científico
Fonte: Proceedings of the American Mathematical Society; v. 145, n. 11, p. 4783-4794, NOV 2017.
Citações Web of Science: 4
Resumo

We study the Schrodinger equations -Delta u + V (x) u = f( x, u) in R-N and -Delta u -lambda u = f( x, u) in a bounded domain Omega subset of R-N. We assume that f is superlinear but of subcritical growth and u bar right arrow f( x, u)/vertical bar u vertical bar is nondecreasing. In R-N we also assume that V and f are periodic in x1,..., xN. We show that these equations have a ground state and that there exist infinitely many solutions if f is odd in u. Our results generalize those by Szulkin and Weth {[}J. Funct. Anal. 257 (2009), 3802- 3822], where u bar right arrow f( x, u)/vertical bar u vertical bar was assumed to be strictly increasing. This seemingly small change forces us to go beyond methods of smooth analysis. (AU)

Processo FAPESP: 15/10545-0 - Problemas Elípticos com Pesos Indefinidos
Beneficiário:Francisco Odair Vieira de Paiva
Modalidade de apoio: Bolsas no Exterior - Pesquisa