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

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