Displaying similar documents to “Fixed points for discontinuous monotone operators.”

On discontinuous implicit differential equations in ordered Banach spaces with discontinuous implicit boundary conditions

S. Carl, S. Heikkilä (1999)

Annales Polonici Mathematici

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We consider the existence of extremal solutions to second order discontinuous implicit ordinary differential equations with discontinuous implicit boundary conditions in ordered Banach spaces. We also study the dependence of these solutions on the data, and cases when the extremal solutions are obtained as limits of successive approximations. Examples are given to demonstrate the applicability of the method developed in this paper.

Hybrid fixed point theory for right monotone increasing multi-valued mappings and neutral functional differential inclusions

Bapurao Chandra Dhage (2007)

Archivum Mathematicum

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In this paper, some hybrid fixed point theorems for the right monotone increasing multi-valued mappings in ordered Banach spaces are proved via measure of noncompactness and they are further applied to the neutral functional nonconvex differential inclusions involving discontinuous multi-functions for proving the existence results under mixed Lipschitz, compactness and right monotonicity conditions. Our results improve the multi-valued hybrid fixed point theorems of Dhage (Dhage, B....

Monotone operators. A survey directed to applications to differential equations

Jan Franců (1990)

Aplikace matematiky

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The paper deals with the existence of solutions of the form A u = b with operators monotone in a broader sense, including pseudomonotone operators and operators satisfying conditions S and M . The first part of the paper which has a methodical character is concluded by the proof of an existence theorem for the equation on a reflexive separable Banach space with a bounded demicontinuous coercive operator satisfying condition ( M ) 0 . The second part which has a character of a survey compares various...