Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/16195
 Title: Nonlinear, nonhomogeneous parametric Neumann problems Author: Aizicovici, S.Papageorgiou, Nikolaos S.Staicu, Vasile Keywords: Positive solutionsNonlinear nonhomogeneous differential operatorNonlinear regularityNonlinear maximum principleBifurcation type resultNodal 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 URI: http://hdl.handle.net/10773/16195 DOI: 10.12775/TMNA.2016.035 ISSN: 1230-3429 Appears in Collections: CIDMA - ArtigosFAAG - Artigos

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