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A variational approach to multiplicity results for boundary-value problems on the real line

Published online by Cambridge University Press:  30 January 2015

Gabriele Bonanno ,
Giuseppina Barletta  and
Donal O’Regan
Gabriele Bonanno
Affiliation:
Department of Civil, Computer, Construction, Environmental Engineering and Applied Mathematics, University of Messina, 98166 Messina, Italy, (bonanno@unime.it)
Giuseppina Barletta
Affiliation:
Dipartimento di Meccanica e Materiali (MECMAT), University of Reggio Calabria, 89100 Reggio Calabria, Italy
Donal O’Regan
Affiliation:
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
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Abstract

We study the existence and multiplicity of solutions for a parametric equation driven by the p-Laplacian operator on unbounded intervals. Precisely, by using a recent local minimum theorem we prove the existence of a non-trivial non-negative solution to an equation on the real line, without assuming any asymptotic condition either at 0 or at ∞ on the nonlinear term. As a special case, we note the existence of a non-trivial solution for the problem when the nonlinear term is sublinear at 0. Moreover, under a suitable superlinear growth at ∞ on the nonlinearity we prove a multiplicity result for such a problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 1 , February 2015 , pp. 13 - 29
Copyright
Copyright © Royal Society of Edinburgh 2015 

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