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Some algebraic fixed point theorems for multi-valued mappings with applications

Bupurao C. Dhage — 2006

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, some algebraic fixed point theorems for multi-valued discontinuous operators on ordered spaces are proved. These theorems improve the earlier fixed point theorems of Dhage (1988, 1991) Dhage and Regan (2002) and Heikkilä and Hu (1993) under weaker conditions. The main fixed point theorems are applied to the first order discontinuous differential inclusions for proving the existence of the solutions under certain monotonicity condition of multi-functions.

The method of upper and lower solutions for perturbed nth order differential inclusions

Bupurao C. Dhage;  Adrian Petruşel — 2006

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, an existence theorem for nth order perturbed differential inclusion is proved under the mixed Lipschitz and Carathéodory conditions. The existence of extremal solutions is also obtained under certain monotonicity conditions on the multi-functions involved in the inclusion. Our results extend the existence results of Dhage et al. [7,8] and Agarwal et al. [1].

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