Qualitative Phenomena for Some Classes of Quasilinear Elliptic Equations with Multiple Resonance

Qualitative Phenomena for Some Classes of Quasilinear Elliptic Equations with Multiple Resonance We consider nonlinear nonhomogeneous Dirichlet problems driven by the sum of a p -Laplacian and a Laplacian. The hypotheses on the reaction term incorporate problems resonant at both ±∞ and zero. We consider both cases p >2 and 1< p <2 (singular case) and we prove four multiplicity theorems producing three or four nontrivial solutions. For the case p >2 we provide precise sign information for all the solutions. Our approach uses critical point theory, truncation and comparison techniques, Morse theory and the Lyapunoff-Schmidt reduction method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Qualitative Phenomena for Some Classes of Quasilinear Elliptic Equations with Multiple Resonance

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Publisher
Springer US
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-013-9227-z
Publisher site
See Article on Publisher Site

Abstract

We consider nonlinear nonhomogeneous Dirichlet problems driven by the sum of a p -Laplacian and a Laplacian. The hypotheses on the reaction term incorporate problems resonant at both ±∞ and zero. We consider both cases p >2 and 1< p <2 (singular case) and we prove four multiplicity theorems producing three or four nontrivial solutions. For the case p >2 we provide precise sign information for all the solutions. Our approach uses critical point theory, truncation and comparison techniques, Morse theory and the Lyapunoff-Schmidt reduction method.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jun 1, 2014

References

  • On p -superlinear equations with a nonhomogeneous differential operator
    Aizicovici, S.; Papageorgiou, N.S.; Staicu, V.

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