Sign-Changing Solutions for Nonlinear Elliptic Problems Depending on Parameters
Joint Authors
Motreanu, Dumitru
Carl, Siegfried
Source
International Journal of Differential Equations
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-33, 33 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-02-09
Country of Publication
Egypt
No. of Pages
33
Main Subjects
Abstract EN
The study of multiple solutions for quasilinear elliptic problems under Dirichlet or nonlinear Neumann type boundary conditions has received much attention over the last decades.
The main goal of this paper is to present multiple solutions results for elliptic inclusions of Clarke's gradient type under Dirichlet boundary condition involving the p-Laplacian which, in general, depend on two parameters.
Assuming different structure and smoothness assumptions on the nonlinearities generating the multivalued term, we prove the existence of multiple constant-sign and sign-changing (nodal) solutions for parameters specified in terms of the Fučik spectrum of the p-Laplacian.
Our approach will be based on truncation techniques and comparison principles (sub-supersolution method) for elliptic inclusions combined with variational and topological arguments for, in general, nonsmooth functionals, such as, critical point theory, Mountain Pass Theorem, Second Deformation Lemma, and the variational characterization of the “beginning”of the Fučik spectrum of the p-Laplacian.
In particular, the existence of extremal constant-sign solutions and their variational characterization as global (resp., local) minima of the associated energy functional will play a key-role in the proof of sign-changing solutions.
American Psychological Association (APA)
Carl, Siegfried& Motreanu, Dumitru. 2010. Sign-Changing Solutions for Nonlinear Elliptic Problems Depending on Parameters. International Journal of Differential Equations،Vol. 2010, no. 2010, pp.1-33.
https://search.emarefa.net/detail/BIM-479506
Modern Language Association (MLA)
Carl, Siegfried& Motreanu, Dumitru. Sign-Changing Solutions for Nonlinear Elliptic Problems Depending on Parameters. International Journal of Differential Equations No. 2010 (2010), pp.1-33.
https://search.emarefa.net/detail/BIM-479506
American Medical Association (AMA)
Carl, Siegfried& Motreanu, Dumitru. Sign-Changing Solutions for Nonlinear Elliptic Problems Depending on Parameters. International Journal of Differential Equations. 2010. Vol. 2010, no. 2010, pp.1-33.
https://search.emarefa.net/detail/BIM-479506
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-479506