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Mild solutions of non‐Lipschitz stochastic integrodifferential evolution equations
Author(s) -
Diop Mamadou Abdoul,
Caraballo Tomás,
Mané Aziz
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3879
Subject(s) - mathematics , lipschitz continuity , complement (music) , uniqueness , resolvent , mathematical analysis , work (physics) , thermodynamics , biochemistry , chemistry , physics , complementation , gene , phenotype
In this work, we study the existence and uniqueness of mild solutions for stochastic partial integrodifferential equations under local non‐Lipschitz conditions on the coefficients. Our analysis makes use of the theory of resolvent operators as developed by R. Grimmer as well as a stopping time technique. Our results complement and improve several earlier related works. An example is provided to illustrate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.