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Sequences of Weak Solutions for Non-Local Elliptic Problems with Dirichlet Boundary Condition

Published online by Cambridge University Press:  16 April 2014

Giovanni Molica Bisci  and
Pasquale F. Pizzimenti
Giovanni Molica Bisci
Affiliation:
Department PAU, University of Reggio Calabria, Via Melissari, 89124 Reggio Calabria, Italy, (xlink:href="[email protected]">[email protected])
Pasquale F. Pizzimenti
Affiliation:
Department of Mathematics, University of Messina, Contrada Papardo, Salita Sperone 31, 98166 Messina, Italy, (xlink:href="[email protected]">[email protected])
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Abstract

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In this paper the existence of infinitely many solutions for a class of Kirchhoff-type problems involving the p-Laplacian, with p > 1, is established. By using variational methods, we determine unbounded real intervals of parameters such that the problems treated admit either an unbounded sequence of weak solutions, provided that the nonlinearity has a suitable behaviour at ∞, or a pairwise distinct sequence of weak solutions that strongly converges to 0 if a similar behaviour occurs at 0. Some comparisons with several results in the literature are pointed out. The last part of the work is devoted to the autonomous elliptic Dirichlet problem.

Keywords

Critical pointweak solutionsKirchhoff-type problemsmultiple solutionsPrimary 35J9235J6046N20
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 3 , October 2014 , pp. 779 - 809
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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