Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity

Calogero Vetro; Francesca Vetro; Nikolaos S. Papageorgiou

Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity

Calogero Vetro, Francesca Vetro, Nikolaos S. Papageorgiou

Matematica e Informatica

Risultato della ricerca: Article › peer review

1 Citazioni (Scopus)

Abstract

We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Caratheodory reaction term which is resonant both at zero and ± ∞. Using the Lyapunov–Schmidt reduction method and critical groups (Morse theory), we show that the problem has at least two nontrivial smooth solutions.

Lingua originale	English
pagine (da-a)	487-503
Numero di pagine	17
Rivista	Manuscripta Mathematica
Volume	158
Stato di pubblicazione	Published - 2019

All Science Journal Classification (ASJC) codes

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title = "Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity",

abstract = "We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Caratheodory reaction term which is resonant both at zero and ± ∞. Using the Lyapunov–Schmidt reduction method and critical groups (Morse theory), we show that the problem has at least two nontrivial smooth solutions.",

author = "Calogero Vetro and Francesca Vetro and Papageorgiou, {Nikolaos S.}",

year = "2019",

language = "English",

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pages = "487--503",

journal = "Manuscripta Mathematica",

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T1 - Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity

AU - Vetro, Calogero

AU - Vetro, Francesca

AU - Papageorgiou, Nikolaos S.

PY - 2019

Y1 - 2019

N2 - We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Caratheodory reaction term which is resonant both at zero and ± ∞. Using the Lyapunov–Schmidt reduction method and critical groups (Morse theory), we show that the problem has at least two nontrivial smooth solutions.

AB - We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Caratheodory reaction term which is resonant both at zero and ± ∞. Using the Lyapunov–Schmidt reduction method and critical groups (Morse theory), we show that the problem has at least two nontrivial smooth solutions.

UR - http://hdl.handle.net/10447/345082

UR - https://link.springer.com/article/10.1007/s00229-018-1044-x

M3 - Article

VL - 158

SP - 487

EP - 503

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

ER -