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May 2017 Triple solutions for quasilinear one-dimensional p-Laplacian elliptic equations in the whole space
Gabriele Bonanno, Donal O’Regan, Francesca Vetro
Ann. Funct. Anal. 8(2): 248-258 (May 2017). DOI: 10.1215/20088752-0000010X

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.

Citation

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Gabriele Bonanno. Donal O’Regan. Francesca Vetro. "Triple solutions for quasilinear one-dimensional p-Laplacian elliptic equations in the whole space." Ann. Funct. Anal. 8 (2) 248 - 258, May 2017. https://doi.org/10.1215/20088752-0000010X

Information

Received: 2 August 2016; Accepted: 16 September 2016; Published: May 2017
First available in Project Euclid: 1 March 2017

zbMATH: 06694413
MathSciNet: MR3619320
Digital Object Identifier: 10.1215/20088752-0000010X

Subjects:
Primary: 34B40
Secondary: 47H14, 49J40

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.8 • No. 2 • May 2017
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