Annals of Functional Analysis

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

Gabriele Bonanno, Donal O’Regan, and Francesca Vetro

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34B40: Boundary value problems on infinite intervals
Secondary: 47H14: Perturbations of nonlinear operators [See also 47A55, 58J37, 70H09, 70K60, 81Q15] 49J40: Variational methods including variational inequalities [See also 47J20]

nonlinear differential problems in unbounded domains operators without compactness critical points three solutions


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.

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