Xie, XumingAlmashaan, Sahar2018-10-252018-10-252018http://hdl.handle.net/11603/11731In 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 .enThis item is made available by Morgan State University for personal, educational, and research purposes in accordance with Title 17 of the U.S. Copyright Law. Other uses may require permission from the copyright owner.MathematicsText