0000000000108897

AUTHOR

Emilio Vilches

showing 2 related works from this author

Constrained differential inclusions with nonlocal initial conditions

2017

International audience; We show existence for the perturbed sweeping process with nonlocal initial conditions under very general hypotheses. Periodic, anti-periodic, mean value and multipoints conditions are included in this study. We give abstract results for differential inclusions with nonlocal initial conditions through bounding functions and tangential conditions. Some applications to differential complementarity systems and to vector hysteresis are given.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]MSC: 34A60 49J52 34G25 49J53 34B10Periodic solutionsNonlocal Cauchy problemDifferential inclusions[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Sweeping processesNormal coneBounding functions
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Positively $\alpha$-Far Sets and Existence Results for Generalized Perturbed Sweeping Processes

2016

International audience; We consider the general class of positively alpha-far sets, introduced in [29], which contains strictly the class of uniformly prox-regular sets and the class of uniformly subsmooth sets. We provide some conditions to assure the uniform subsmoothness, and thus the positive alpha-farness, of the inverse images under a differentiable mapping. Then, we take advantage of the properties of this class to study the generalized perturbed sweeping process{-(x)over dot(t) is an element of F(t, x(t))+ g(x(t))N (C(t), h(x(t))) a.e. t is an element of[T-0, T], x(T-0) = x(0) is an element of h(-1) (C(T-0)), where g : X -> L(Y; X), h: X -> Y are two functions, X, Y are two separabl…

[ MATH ] Mathematics [math][MATH] Mathematics [math][MATH]Mathematics [math]
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