Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (6): 1803-1816.doi: 10.1016/S0252-9602(17)30108-X

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SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS FOR THE NON-NEWTONIAN FILTRATION EQUATIONS WITH NONLINEAR SOURCES AND A TIME-VARYING DELAY

Fanchao KONG, Zhiguo LUO   

  1. Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP)(Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China
  • Received:2016-06-07 Revised:2016-10-30 Online:2017-12-25 Published:2017-12-25
  • Supported by:

    The research was supported by the National Natural Science Foundation of China (11471109), the Construct Program of the Key Discipline in Hunan Province and Hunan Provincial Innovation Foundation for Postgraduate (CX2017B172).

Abstract:

This paper is concerned with the non-Newtonian filtration equations with nonlinear sources and a time-varying delay. By an extension of Mawhin's continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results.

Key words: solitary wave, periodic wave, Mawhin's continuation theorem, time-varying delay, nonlinear sources

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