We consider nonlinear Neumann problems driven by the $p$-Laplacian plus an indefinite potential. First we develop the spectral properties of such differential operators. Subsequently, using these spectral properties and variational methods based on critical point theory, truncation techniques and Morse theory, we prove existence and multiplicity theorems for resonant problems.
@article{ASNSP_2012_5_11_4_729_0, author = {Mugnai, Dimitri and Papageorgiou, Nikolaos S.}, title = {Resonant nonlinear Neumann problems with indefinite weight}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {4}, year = {2012}, pages = {729-788}, zbl = {1270.35215}, mrnumber = {3060699}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2012_5_11_4_729_0} }
Mugnai, Dimitri; Papageorgiou, Nikolaos S. Resonant nonlinear Neumann problems with indefinite weight. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 4, pp. 729-788. http://www.numdam.org/item/ASNSP_2012_5_11_4_729_0/
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