Multiple positive solutions of a nonlinear fourth order periodic boundary value problem

Volume 69 / 1998

Lingbin Kong, Daqing Jiang Annales Polonici Mathematici 69 (1998), 265-270 DOI: 10.4064/ap-69-3-265-270

Abstract

The fourth order periodic boundary value problem $u^{(4)} - m⁴u + F(t,u) = 0$, 0 < t < 2π, with $u^{(i)}(0) = u^{(i)}(2π)$, i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of $±10^{-7}$.

Authors

  • Lingbin Kong
  • Daqing Jiang

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