Nonlinear, nonhomogeneous parametric Neumann problems

• Autor(a) principal: Aizicovici, S.
• Data de Publicação: 2016
• Outros Autores: Papageorgiou, Nikolaos S., Staicu, Vasile
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/16195
• topic: Positive solutions; Nonlinear nonhomogeneous differential operator; Nonlinear regularity; Nonlinear maximum principle; Bifurcation type result; Nodal solutions

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.