Systems of differential inclusions in the absence of maximum principles and growth conditions

Tisdell, Christopher

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 26 (2006) no. 1, pp. 129-141.

Résumé

This article investigates the existence of solutions to second-order boundary value problems (BVPs) for systems of ordinary differential inclusions. The boundary conditions may involve two or more points. Some new inequalities are presented that guarantee a priori bounds on solutions to the differential inclusion under consideration. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow the treatment of systems of BVPs in the absence of maximum principles and growth conditions. The results are also new for differential equations involving Carathéodory or even continuous right-hand sides.

Détail

Keywords: boundary value problem, systems of differential inclusions, existence of solutions, a priori bounds, two-point boundary conditions, three-point boundary conditions

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