We consider a nonlinear Robin problem associated to the p-Laplacian plus an indefinitepotential. In the reaction we have the competing effects of two nonlinear terms. Oneis parametric and strictly ( p − 1)-sublinear. The other is ( p − 1)-linear. We prove abifurcation-type theorem describing the dependence of the set of positive solutions onthe parameter λ>0. We also show that for every admissible parameter the problem hasa smallest positive solution ¯uλand we study monotonicity and continuity propertiesof the map λ →¯uλ.

Positive solutions for nonlinear Robin problems with indefinite potential and competing nonlinearities

Leonardi, S
;
2020

Abstract

We consider a nonlinear Robin problem associated to the p-Laplacian plus an indefinitepotential. In the reaction we have the competing effects of two nonlinear terms. Oneis parametric and strictly ( p − 1)-sublinear. The other is ( p − 1)-linear. We prove abifurcation-type theorem describing the dependence of the set of positive solutions onthe parameter λ>0. We also show that for every admissible parameter the problem hasa smallest positive solution ¯uλand we study monotonicity and continuity propertiesof the map λ →¯uλ.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/362184
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