We consider a parametric nonlinear Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential. The reaction term is (p- 1) -superlinear but need not satisfy the usual Ambrosetti–Rabinowitz condition. We look for positive solutions and prove a bifurcation-type result for the set of positive solutions as the parameter λ> 0 varies. Also we prove the existence of a minimal positive solution uλ∗ and determine the monotonicity and continuity properties of the map λ→uλ∗.
Papageorgiou N.S., Vetro C., Vetro F. (2020). Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES. SERIE A, MATEMÁTICAS, 114(1), 1-29 [10.1007/s13398-019-00779-1].
Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems
Vetro C.;
2020-01-01
Abstract
We consider a parametric nonlinear Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential. The reaction term is (p- 1) -superlinear but need not satisfy the usual Ambrosetti–Rabinowitz condition. We look for positive solutions and prove a bifurcation-type result for the set of positive solutions as the parameter λ> 0 varies. Also we prove the existence of a minimal positive solution uλ∗ and determine the monotonicity and continuity properties of the map λ→uλ∗.
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