An existence and uniqueness result for periodic solution of 2n-order differential equations

  • Authors:

  • Xiaojing Yang

  • Affiliations:

  • Department of Mathematics, Tsinghua University, Beijing 100084, People's Republic of China

  • Venue:
  • Applied Mathematics and Computation
  • Year:
  • 2003

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Abstract

In this paper, we are concerned with the existence and uniqueness of solution to the 2n-order differential equation (-1)n-1x(2n) + f(t,x,x'', .... x2(n-1)) = 0 with periodic boundary condition x(i)(0) = x(i)(2π), i = 0, 1,...,2n - 1. By using the initial value problem method, we transform the periodic boundary value problem into a problem of finding fixed point of continuous mapping.