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 subsupersolution 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.
Motreanu D., Sciammetta A., Tornatore E. (2020). A sub-supersolution approach for robin boundary value problems with full gradient dependence. MATHEMATICS, 8(5), 1-13 [10.3390/MATH8050658].
A sub-supersolution approach for robin boundary value problems with full gradient dependence
Motreanu D.
;Sciammetta A.;Tornatore E.
2020-01-01
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 subsupersolution 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.
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