6533b85ffe1ef96bd12c27c3
RESEARCH PRODUCT
Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems
Nikolaos S. PapageorgiouCalogero VetroFrancesca Vetrosubject
Pure mathematicsAlgebra and Number TheoryApplied MathematicsMathematics::Analysis of PDEsMonotonic functionNonlinearDifferential operatorLambdaBifurcation-type resultTerm (time)Positive solutionSet (abstract data type)Computational MathematicsNonlinear systemSettore MAT/05 - Analisi MatematicaIndefinite potentialNonhomogeneous differential operatorGeometry and TopologySuperlinear reaction termAnalysisNonlinear regularity theoryParametric statisticsMathematicsdescription
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 $$\lambda >0$$ varies. Also we prove the existence of a minimal positive solution $$u_\lambda ^*$$ and determine the monotonicity and continuity properties of the map $$\lambda \rightarrow u_\lambda ^*$$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-01-01 | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas |