Wang’s multiplicity result for superlinear $(p,q)$–equations without the Ambrosetti–Rabinowitz condition
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- by Dimitri Mugnai and Nikolaos S. Papageorgiou PDF
- Trans. Amer. Math. Soc. 366 (2014), 4919-4937 Request permission
Abstract:
We consider a nonlinear elliptic equation driven by the sum of a $p$–Laplacian and a $q$–Laplacian, where $1<q\leq 2\leq p<\infty$ with a $(p-1)$–superlinear Carathéodory reaction term which doesn’t satisfy the usual Ambrosetti–Rabinowitz condition. Using variational methods based on critical point theory together with techniques from Morse theory, we show that the problem has at least three nontrivial solutions; among them one is positive and one is negative.References
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Additional Information
- Dimitri Mugnai
- Affiliation: Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy
- Email: mugnai@dmi.unipg.it
- Nikolaos S. Papageorgiou
- Affiliation: Department of Mathematics, National Technical University, Zografou Campus, Athens 15780 Greece
- MR Author ID: 135890
- Email: npapg@math.ntua.gr
- Received by editor(s): August 6, 2012
- Received by editor(s) in revised form: January 23, 2013
- Published electronically: October 28, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 4919-4937
- MSC (2010): Primary 35J20; Secondary 35J60, 35J92, 58E05
- DOI: https://doi.org/10.1090/S0002-9947-2013-06124-7
- MathSciNet review: 3217704