2004
DOI: 10.1023/b:svan.0000031356.03559.91
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Existence Results on the Second-Order Nonconvex Sweeping Processes with Perturbations

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Cited by 41 publications
(32 citation statements)
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“…Later, Bounkhel and Yarou [4] proved in the infinite-dimensional setting the existence of solutions in the case the set-valued map G has all its valued contained in a fixed compact set. More recently, we proved in [13] a more general result where G satisfies (0.4) with B replaced by a fixed compact set.…”
Section: Introductionmentioning
confidence: 98%
“…Later, Bounkhel and Yarou [4] proved in the infinite-dimensional setting the existence of solutions in the case the set-valued map G has all its valued contained in a fixed compact set. More recently, we proved in [13] a more general result where G satisfies (0.4) with B replaced by a fixed compact set.…”
Section: Introductionmentioning
confidence: 98%
“…We point out that the compactness assumption on C is not needed in the Hilbert space. A second order version of (1.2) has been the subject of various papers (see for instance [5,6,10]). The last and recent extension of (SDI), (accordingly to our best knowledge), has been given in [5], in which the author proved the existence of solution for the following general extension of (SDI)…”
Section: Introductionmentioning
confidence: 99%
“…The existence of solutions for the second-order sweeping process has been thoroughly studied in the literature; see for example [1][2][3][4][5][6][7]. By using an important result of the coincidence between the solutions sets of a constrained and an unconstrained first-order differential inclusion proved in [8,9], we give a new proof of the perturbed second-order sweeping process which improves the ones given in [1][2][3]7].…”
Section: Introductionmentioning
confidence: 91%
“…By using an important result of the coincidence between the solutions sets of a constrained and an unconstrained first-order differential inclusion proved in [8,9], we give a new proof of the perturbed second-order sweeping process which improves the ones given in [1][2][3]7]. …”
Section: Introductionmentioning
confidence: 94%