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Volume 6, Issue 5, 1 October 2022, Pages 585-599
Abstract. Let , , and be a lower semicontinuos and bounded multifunction with nonempty closed values. We prove that there exists a bounded and upper semicontinuous multifunction with nonempty compact convex values such that every generalized solution of the differential inclusion is a generalized solution to the differential inclusion . As an application, we prove an existence and qualitative result for the generalized solutions of the Cauchy problem associated to the inclusion . In particular, we prove that if is lower semicontinuous and bounded with nonempty closed values, then the solution multifunction admits an upper semicontinuous multivalued selection with nonempty compact connected values. Finally, by applying the latter result, we prove an analogous existence and qualitative result for the generalized solutions of the Cauchy problem associated to the differential equation , where is continuous. We only assume that is continuous and locally nonconstant.
How to Cite this Article:
Paolo Cubiotti, Jen-Chih Yao, Some qualitative properties of solutions of higher-order lower semicontinus differential inclusions, J. Nonlinear Var. Anal. 6 (2022), 585-599.