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Title: Nonlinear, nonhomogeneous parametric Neumann problems
Author: Aizicovici, S.
Papageorgiou, Nikolaos S.
Staicu, Vasile
Keywords: Positive solutions
Nonlinear nonhomogeneous differential operator
Nonlinear regularity
Nonlinear maximum principle
Bifurcation type result
Nodal solutions
Issue Date: Sep-2016
Publisher: Juliusz Schauder University Centre for Nonlinear Studies; Nicolaus Copernicus University in Toruń
Abstract: We consider a parametric nonlinear Neumann problem driven by a nonlinear nonhomogeneous differential operator and with a Caratheodory reaction $f\left( t,x\right) $ which is $p-$superlinear in $x$ without satisfying the usual in such cases Ambrosetti-Rabinowitz condition. We prove a bifurcation type result describing the dependence of the positive solutions on the parameter $\lambda>0,$ we show the existence of a smallest positive solution $\overline{u}_{\lambda}$ and investigate the properties of the map $\lambda\rightarrow\overline{u}_{\lambda}.$ Finally we also show the existence of nodal solutions.
Peer review: yes
DOI: 10.12775/TMNA.2016.035
ISSN: 1230-3429
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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