Paolo Cubiotti, Jen-Chih Yao, Some qualitative properties of solutions of higher-order lower semicontinus differential inclusions
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DOI: 10.23952/jnva.6.2022.5.10
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.