Abstract
This paper is concerned with the problem of existence of solutions to the initial value problemu′(t) = A(t,u(t)), u(a) = z in a probabilistic normed space, whereA : [a, b) × D → E is continuous,D is a closed subset of a probabilistic normed spaceE, andz ∃ D. With a dissipative type condition onA, we estabilish sufficient conditions for this initial value problem to have a solution.
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Kim, J.K., Jin, B.J. Differential equations on closed subsets of a probabilistic normed space. Korean J. Comput. & Appl. Math. 5, 223–233 (1998). https://doi.org/10.1007/BF03008951
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DOI: https://doi.org/10.1007/BF03008951