A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence

Dumitru Motreanu, Angela Sciammetta and Elisabetta Tornatore
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Dumitru Motreanu: Department of Mathematics, University of Perpignan, 66860 Perpignan, France
Angela Sciammetta: Department of Mathematics and Computer Science, University of Palermo, 90123 Palermo, Italy
Elisabetta Tornatore: Department of Mathematics and Computer Science, University of Palermo, 90123 Palermo, Italy

Mathematics, 2020, vol. 8, issue 5, 1-13

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.

Keywords: nonlinear elliptic problem; Robin boundary condition; gradient dependence; sub-supersolution; positive solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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