A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence
Dumitru Motreanu, Angela Sciammetta, Elisabetta Tornatore
Abstract
The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems. The main result establishes the existence of a solution enclosed in the ordered interval formed by a sub-supersolution. The result is applied to find positive solutions.
Topics & Concepts
Boundary value problemNonlinear systemInterval (graph theory)Boundary (topology)MathematicsTerm (time)Value (mathematics)Mathematical analysisApplied mathematicsPhysicsCombinatoricsStatisticsQuantum mechanicsAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsDifferential Equations and Numerical Methods