## Annals of Functional Analysis

### Triple solutions for quasilinear one-dimensional $p$-Laplacian elliptic equations in the whole space

#### 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.

#### Article information

Source
Ann. Funct. Anal., Volume 8, Number 2 (2017), 248-258.

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1488358820

Digital Object Identifier
doi:10.1215/20088752-0000010X

Mathematical Reviews number (MathSciNet)
MR3619320

Zentralblatt MATH identifier
06694413

#### Citation

Bonanno, Gabriele; O’Regan, Donal; Vetro, Francesca. Triple solutions for quasilinear one-dimensional $p$ -Laplacian elliptic equations in the whole space. Ann. Funct. Anal. 8 (2017), no. 2, 248--258. doi:10.1215/20088752-0000010X. https://projecteuclid.org/euclid.afa/1488358820

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