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Nonhomogeneous Nonlinear Dirichlet Problems with a p-Superlinear Reaction
Joint Authors
Papageorgiou, Nikolaos S.
Gasiński, Leszek
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-28, 28 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-05-15
Country of Publication
Egypt
No. of Pages
28
Main Subjects
Abstract EN
We consider a nonlinear Dirichlet elliptic equation driven by a nonhomogeneous differential operator and with a Carathéodory reaction f(z,ζ), whose primitive f(z,ζ) is p-superlinear near ±∞, but need not satisfy the usual in such cases, the Ambrosetti-Rabinowitz condition.
Using a combination of variational methods with the Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions.
Our result unifies the study of “superlinear” equations monitored by some differential operators of interest like the p-Laplacian, the (p,q)-Laplacian, and the p-generalized mean curvature operator.
American Psychological Association (APA)
Gasiński, Leszek& Papageorgiou, Nikolaos S.. 2012. Nonhomogeneous Nonlinear Dirichlet Problems with a p-Superlinear Reaction. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-508045
Modern Language Association (MLA)
Gasiński, Leszek& Papageorgiou, Nikolaos S.. Nonhomogeneous Nonlinear Dirichlet Problems with a p-Superlinear Reaction. Abstract and Applied Analysis No. 2012 (2012), pp.1-28.
https://search.emarefa.net/detail/BIM-508045
American Medical Association (AMA)
Gasiński, Leszek& Papageorgiou, Nikolaos S.. Nonhomogeneous Nonlinear Dirichlet Problems with a p-Superlinear Reaction. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-508045
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-508045