J. Nonl. Evol. Equ. Appl. 2012 (9), pp. 113-128, published on January 2, 2013:

Existence of non-oscillatory solutions for nonlinear differential equations with distributed delays and m-order linear operators with variable coefficients

J. G. Dix

Texas State University, 601 University Drive, San Marcos, TX 78666, USA

Received on July 24, 2012
Accepted on October 25, 2012

Communicated by Alexander Pankov

Abstract.  This article concerns the existence of non-oscillatory solutions for non-linear, non-homogeneous differential equations. In these equations, the unknown function depends on distributed arguments that can be retarded or advanced and have variable delays. Using contraction mappings, we show the existence of solutions, and estimate their norms. Then our results are extended to dynamic equations on times scales, and to difference equations.
Keywords: Neutral equation; non-oscillatory solution; distributed delay.
2010 Mathematics Subject Classification:   34K40, 34K11, 34C10.

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