On nonlocal Cauchy problems for constrained differential inclusions in Euclidean space

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• 作者：Radosław Pietkun ^{pietkunr@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Differential inclusion with constraints ; Generalized gradient ; Topological degree ; Fredholm operator ; Nonlocal boundary value problem ; Floquet problem
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：437
• 期：2
• 页码：941-971
• 全文大小：602 K

文摘

We investigate the existence of solutions of constrained nonlinear differential inclusions with nonlocal boundary conditions. Our viability theorems are based on the assumption that the right-hand side of differential inclusion is defined on the domain possessing a certain type of geometric regularity, expressed in terms of locally Lipschitz functional constraints. For solvability of the Floquet boundary value problems associated with differential inclusions we engage the bound set technique. It relies on the usage of not necessarily differentiable bounding functions.