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}, pages = {729--788}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {4}, year = {2012}, mrnumber = {3060699}, zbl = {1270.35215}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2012_5_11_4_729_0/} }
TY - JOUR AU - Mugnai, Dimitri AU - Papageorgiou, Nikolaos S. TI - Resonant nonlinear Neumann problems with indefinite weight JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 729 EP - 788 VL - 11 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2012_5_11_4_729_0/ LA - en ID - ASNSP_2012_5_11_4_729_0 ER -
%0 Journal Article %A Mugnai, Dimitri %A Papageorgiou, Nikolaos S. %T Resonant nonlinear Neumann problems with indefinite weight %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 729-788 %V 11 %N 4 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2012_5_11_4_729_0/ %G en %F 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://archive.numdam.org/item/ASNSP_2012_5_11_4_729_0/
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