Existence, Uniqueness and Ulam Stabilities for Nonlinear Hyperbolic Partial Integrodifferential Equations

  • Pallavi U. ShikhareEmail author
  • Kishor D. Kucche
Original Paper


In the present article, by employing weakly Picard operator theory we investigate the existence and uniqueness of solutions and Ulam–Hyers stability of nonlinear hyperbolic partial Volterra and Volterra–Fredholm integrodifferential equations in Banach Spaces. Further, we obtain Ulam–Hyers–Rassias stability for these equations via Pachpatte’s integral inequalities. Appropriate examples are provided in support of the results we obtained.


Hyperbolic partial integrodifferential equations Ulam–Hyers stability Ulam–Hyers–Rassias stability Integral inequality Fixed point equation Weakly Picard operator 

Mathematics Subject Classification

34G20 35L90 35R45 45M10 47H10 



The first author is financially supported by UGC, New Delhi, India. Ref: F1-17.1/2017-18/RGNF-2017-18-SC-MAH-43083.


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© Springer Nature India Private Limited 2019

Authors and Affiliations

  1. 1.Department of MathematicsShivaji UniversityKolhapurIndia

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