Existence and stability of a class of nonlinear Volterra integral equations
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- by Stanley I. Grossman PDF
- Trans. Amer. Math. Soc. 150 (1970), 541-556 Request permission
Abstract:
In this paper we study the problem of existence and uniqueness to solutions of the nonlinear Volterra integral equation $x = f + {a_1}{g_1}(x) + \cdots + {a_n}{g_n}(x)$, where the ${a_i}$ are continuous linear operators mapping a Fréchet space $\mathcal {F}$ into itself and the ${g_i}$ are nonlinear operators in that space. Solutions are sought which lie in a Banach subspace of $\mathcal {F}$ having a stronger topology. The equations are studied first when the ${g_i}$ are of the form ${g_i}(x) = x + {h_i}(x)$ where ${h_i}(x)$ is “small", and then when the ${g_i}$ are slope restricted. This generalizes certain results in recent papers by Miller, Nohel, Wong, Sandberg, and Beneš.References
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Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 150 (1970), 541-556
- MSC: Primary 45.30
- DOI: https://doi.org/10.1090/S0002-9947-1970-0265886-8
- MathSciNet review: 0265886