scholarly journals The Brezis–Oswald Result for Quasilinear Robin Problems

2016 ◽  
Vol 16 (3) ◽  
Author(s):  
Genni Fragnelli ◽  
Dimitri Mugnai ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Elliptic Problem ◽  
Robin Boundary Conditions ◽  
Nonlinear Elliptic Problem ◽  
Reaction Term ◽  
Nonhomogeneous Differential Operator ◽  
Nonlinear Elliptic ◽  
Robin Boundary

AbstractIn this paper we consider a nonlinear elliptic problem driven by a nonhomogeneous differential operator with Robin boundary conditions. We produce conditions on the reaction term near

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

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 658 ◽  
Author(s):  
Dumitru Motreanu ◽  
Angela Sciammetta ◽  
Elisabetta Tornatore
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Robin Boundary Condition ◽  
Convection Term ◽  
Nonlinear Elliptic Problem ◽  
Existence Of A Solution ◽  
Nonlinear Elliptic ◽  
Robin Boundary

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.

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