Analytic solution to a class of integro-differential equations
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Date
2003-03-28
Authors
Xie, Xuming
Journal Title
Journal ISSN
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.
Description
Keywords
Analytic solution, Singular integro-differential equation
Citation
Xie, X. (2003). Analytic solution to a class of integro-differential equations. Electronic Journal of Differential Equations, 2003(33), pp. 1-25.
Rights
Attribution 4.0 International