We consider a Robin problem driven by a nonlinear nonhomogeneous differential operator plus a parametric potential term. The reaction is superlinear. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter lambda in R moves. Also we show the existence of a minimal positive solution and prove its monotonicity and continuity properties as a function of the parameter. Finally we show the existence of a nodal solution.
Papaceorgiou, N.S., Vetro, C., Vetro, F. (2022). Parametric nonlinear nonhomogeneous Robin problems. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 23(7), 1289-1310.
Parametric nonlinear nonhomogeneous Robin problems
Vetro, C;
2022-01-01
Abstract
We consider a Robin problem driven by a nonlinear nonhomogeneous differential operator plus a parametric potential term. The reaction is superlinear. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter lambda in R moves. Also we show the existence of a minimal positive solution and prove its monotonicity and continuity properties as a function of the parameter. Finally we show the existence of a nodal solution.
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