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

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Abstract

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.

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Acknowledgements

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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  1. Department of Mathematics, Shivaji University, Kolhapur, Maharashtra, 416 004, India

    Pallavi U. Shikhare & Kishor D. Kucche

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  1. Pallavi U. Shikhare
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  2. Kishor D. Kucche
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Correspondence to Pallavi U. Shikhare.

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Shikhare, P.U., Kucche, K.D. Existence, Uniqueness and Ulam Stabilities for Nonlinear Hyperbolic Partial Integrodifferential Equations. Int. J. Appl. Comput. Math 5, 156 (2019). https://doi.org/10.1007/s40819-019-0742-8

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  • DOI: https://doi.org/10.1007/s40819-019-0742-8

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