Analytic Solution To A Class Of Integro-Differential Equations Of Third Order
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In this work, we consider the integro-differential equation ϵ2y′′′(x) + L(x)y′(x) + E(x)y(x) = N(ϵ2,x,y,H(y)) where H(y)[x] =1\dt is the Hilbert transform. The existence 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 Banach Contraction Mapping Theorem .