Nonlinear Neumann equations driven by a nonhomogeneous differential operator
Abstract
We consider a nonlinear Neumann problem driven by a nonhomogeneous nonlinear differential operator and with a reaction which is (p-1)-superlinear without necessarily satisfying the Ambrosetti-Rabinowitz condition. A particular case of our differential operator is the p-Laplacian. By combining variational methods based on critical point theory with truncation techniques and Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive and the other negative).
Document Type
Article
DOI
https://doi.org/10.3934/cpaa.2011.10.1055
Keywords
nonlinear regularity, morse relation, moser iteration method., Mountain Pass theorem, critical group, C-condition
Publication Date
2011
Recommended Citation
Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Nonlinear Neumann equations driven by a nonhomogeneous differential operator." Communications on Pure & Applied Analysis 10, no. 4 (2011): 1055.
Journal Title
Communications on Pure & Applied Analysis
