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Existence of viable solutions for a nonconvex stochastic differential inclusion

Benoit Truong-Van, Truong Xuan Duc Ha (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

For the stochastic viability problem of the form dx(t) ∈ F(t,x(t))dt+g(t,x(t))dW(t), x(t) ∈ K(t), where K, F are set-valued maps which may have nonconvex values, g is a single-valued function, we establish the existence of solutions under the assumption that F and g possess Lipschitz property and satisfy some tangential conditions.

Existence results for boundary value problems for fourth-order differential inclusions with nonconvex valued right hand side

A. Arara, Mouffak Benchohra, Sotiris K. Ntouyas, Abdelghani Ouahab (2004)

Archivum Mathematicum

In this paper a fixed point theorem due to Covitz and Nadler for contraction multivalued maps, and the Schaefer’s theorem combined with a selection theorem due to Bressan and Colombo for lower semicontinuous multivalued operators with decomposables values, are used to investigate the existence of solutions for boundary value problems of fourth-order differential inclusions.

Existence Results for Fractional Functional Differential Inclusions with Infinite Delay and Applications to Control Theory

Benchohra, M., Henderson, J., Ntouyas, S. K., Ouahab, A. (2008)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 34A60, 34K40, 93B05In this paper we investigate the existence of solutions for fractional functional differential inclusions with infinite delay. In the last section we present an application of our main results in control theory.

Existence results for impulsive fractional differential equations with p -Laplacian via variational methods

John R. Graef, Shapour Heidarkhani, Lingju Kong, Shahin Moradi (2022)

Mathematica Bohemica

This paper presents several sufficient conditions for the existence of at least one classical solution to impulsive fractional differential equations with a p -Laplacian and Dirichlet boundary conditions. Our technical approach is based on variational methods. Some recent results are extended and improved. Moreover, a concrete example of an application is presented.

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