Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (5): 1077-1094.doi: 10.1016/S0252-9602(15)30041-2

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EXISTENCE OF HOMOCLINIC ORBITS FOR A CLASS OF FIRST-ORDER DIFFERENTIAL DIFFERENCE EQUATIONS

Chengjun GUO1, Donal O'REGAN2,3, Yuantong XU4, Ravi P. AGARWAL5,6   

  1. 1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China;
    2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland;
    3. Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;
    4. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China;
    5. Department of Mathematics, Texas A and M University-Kingsville, Texas 78363, USA;
    6. Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
  • Received:2014-01-13 Revised:2014-10-29 Online:2015-09-01 Published:2015-09-01
  • Supported by:

    This project is supported by National Natural Science Foundation of China (51275094), by High-Level Personnel Project of Guangdong Province (2014011) and by China Postdoctoral Science Foundation (20110490893).

Abstract:

In this article we consider via critical point theory the existence of homoclinic orbits of the first-order differential difference equation
?(t)+B(t)z(t)+f(t,z(t+τ),z(t),z(t-τ))=0.

Key words: homoclinic solutions, differential difference equation, critical point theory

CLC Number: 

  • 34K13
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