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On existence of solutions of differential‐difference equations
Authors:Hai‐chou Li
Institution:Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macau, China
Abstract:This paper applies Nevanlinna theory of value distribution to discuss existence of solutions of certain types of non‐linear differential‐difference equations such as (5) and (8) given in the succeeding paragraphs. Existence of solutions of differential equations and difference equations can be said to have been well studied, that of differential‐difference equations, on the other hand, have been paid little attention. Such mixed type equations have great significance in applications. This paper, in particular, generalizes the Rellich–Wittich‐type theorem and Malmquist‐type theorem about differential equations to the case of differential‐difference equations. Copyright © 2015 John Wiley & Sons, Ltd.
Keywords:Nevanlinna theory  complex differential‐difference equations  Rellich–  Wittich‐type theorem  Malmquist‐type theorem
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