Triple solutions for Quasilinear one-dimensional p-laplacian elliptic equations in the whole space

Gabriele Bonanno; Donal O'regan; Francesca Vetro

doi:10.1215/20088752-0000010X

Triple solutions for Quasilinear one-dimensional p-laplacian elliptic equations in the whole space

Gabriele Bonanno, Donal O'regan, Francesca Vetro

Mathematics

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7 Citations (Scopus)

Abstract

In this paper, we establish the existence of three possibly nontrivial solutions for a Dirichlet problem on the real line without assuming on the nonlinearity asymptotic conditions at infinity. As a particular case, when the nonlinearity is superlinear at zero and sublinear at infinity, the existence of two nontrivial solutions is obtained. This approach is based on variational methods and, more precisely, a critical points theorem, which assumes a more general condition than the classical Palais-Smale condition, is exploited.

Original language	English
Pages (from-to)	248-258
Number of pages	11
Journal	Annals of Functional Analysis
Volume	8
Issue number	2
DOIs	https://doi.org/10.1215/20088752-0000010X
Publication status	Published - 1 May 2017

Keywords

Critical points
Nonlinear differential problems in unbounded domains
Operators without compactness
Three solutions

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Bonanno, G;O'Regan, D;Vetro, F

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10.1215/20088752-0000010X

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abstract = "In this paper, we establish the existence of three possibly nontrivial solutions for a Dirichlet problem on the real line without assuming on the nonlinearity asymptotic conditions at infinity. As a particular case, when the nonlinearity is superlinear at zero and sublinear at infinity, the existence of two nontrivial solutions is obtained. This approach is based on variational methods and, more precisely, a critical points theorem, which assumes a more general condition than the classical Palais-Smale condition, is exploited.",

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N2 - In this paper, we establish the existence of three possibly nontrivial solutions for a Dirichlet problem on the real line without assuming on the nonlinearity asymptotic conditions at infinity. As a particular case, when the nonlinearity is superlinear at zero and sublinear at infinity, the existence of two nontrivial solutions is obtained. This approach is based on variational methods and, more precisely, a critical points theorem, which assumes a more general condition than the classical Palais-Smale condition, is exploited.

AB - In this paper, we establish the existence of three possibly nontrivial solutions for a Dirichlet problem on the real line without assuming on the nonlinearity asymptotic conditions at infinity. As a particular case, when the nonlinearity is superlinear at zero and sublinear at infinity, the existence of two nontrivial solutions is obtained. This approach is based on variational methods and, more precisely, a critical points theorem, which assumes a more general condition than the classical Palais-Smale condition, is exploited.

KW - Critical points

KW - Nonlinear differential problems in unbounded domains

KW - Operators without compactness

KW - Three solutions

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DO - 10.1215/20088752-0000010X

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ER -

Triple solutions for Quasilinear one-dimensional p-laplacian elliptic equations in the whole space

Abstract

Keywords

Authors (Note for portal: view the doc link for the full list of authors)

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