Abstract
We prove some existence and uniqueness results for nonlinear stochastic integral equation of Urysohn type using fixed point theory methods. We also establish the stability of the unique solution with respect to small perturbations of the stochastic free term (Constantin, Qualitative problems for differential equations and control theory, World Scientific Publishing, Singapore, 1995).
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References
Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, New York (2011)
Constantin, A.: Some existence results for nonlinear integral equations. In: Corduneanu, C. (ed.) Qualitative Problems for Differential Equations and Control Theory, pp. 105–111. World Scientific Publishing, Singapore (1995)
Constantin, A.: A random integral equation with applications. Indian. J. Math. 37(2), 151–163 (1995)
Constantin, G., Negrea, R.: An application of Schauder’s fixed point theorem in stochastic McShane modeling. J. Fixed Point Theory 5, 37–52 (2004)
Granas, A., Dugundji, J.: Fixed Point Theory. Springer, New York (2003)
Lang, S.: Real and Functional Analysis. Springer, New York (1993)
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The author is grateful to the referee for constructive suggestions and comments.
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Communicated by Adrian Constantin.
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Negrea, R. On a nonlinear stochastic integral equation. Monatsh Math 192, 905–914 (2020). https://doi.org/10.1007/s00605-019-01353-y
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DOI: https://doi.org/10.1007/s00605-019-01353-y