Analytic solution to a class of integro-differential equations

Date

2003-03-28

Authors

Xie, Xuming

Journal Title

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Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

In this paper we consider the integro-differential equation ∈2y''(x) + L(x) H(y) = N(∈, x, y, H(y)), where H(y) [x] = 1/π(P) ∫∞-∞ y(t)/t-x dt is the Hilbert transform. The existence and uniqueness of analytic solution in appropriately chosen space is proved. Our method consists of extending the equation to an appropriately chosen region in the complex plane, then use the Contraction Mapping Theorem.

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Keywords

Analytic solution, Singular integro-differential equation

Citation

Xie, X. (2003). Analytic solution to a class of integro-differential equations. <i>Electronic Journal of Differential Equations, 2003</i>(33), pp. 1-25.

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Attribution 4.0 International

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