Journal of East China Normal University(Natural Sc

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Homoclinic solutions for prescribed mean curvature p-Laplacian equations with delays

KONG Fan-chao[1] , LI-Xun[2] , LU Shi-ping[3]   

  1. 1. Department of Mathematics, Hunan Normal University, Changsha 410081, China;
    2. School of Mathematics and Computer Science, Anhui Normal University, Wuhu Anhui 241000, China;
    3. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
  • Received:2015-06-09 Online:2016-07-25 Published:2016-09-29

Abstract:

In this paper, by applying Mawhin’s continuation theorem, some sufficient conditions on the existence of 2kT-periodic solutions for a kind of prescribed mean curvature Rayleigh p-Laplacian equation with delays are given. Then the existence of nontrivial homoclinic solutions for prescribed mean curvature Rayleigh p-Laplacian equation with delays is obtained. At last, an example is also given to illustrate the application of our main results.

Key words: prescribed mean curvature equation, homoclinic solutions, continuation theorem, p-Laplacian equation, delay