Existence of solutions for 2mth-order periodic boundary value problems

  • Feng X
  • Niu P
  • Guo Q
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Abstract

In this paper, the existence results of solutions are obtained for the 2mth-order differential equation periodic boundary value problem: (-1)mu(2m)(t)+∑i=1m(-1)m-iaiu(2(m-i))(t)=f(t,u(t)) for all t ∈ [0, 1] with u(i)(0) = u(i)(1), i = 0, 1, ⋯, 2m - 1, where f∈C1([0, 1]×ℝ1,ℝ1),ai∈ℝ1,i=1,2,⋯,m. By using the Morse theory, we impose certain conditions on f which are able to guarantee that the problem has at least one nontrivial solution, two nontrivial solutions and infinitely many solutions, separately. © 2011 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • 2mth-order PBVP
  • Critical group
  • Morse theory
  • Nontrivial solutions

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