Multiple positive solutions for nonlinear dynamical systems on a measure chain

作者：Li WT^*; Sun HR

来源：Journal of Computational and Applied Mathematics, 2004, 162(2): 421-430.

DOI：10.1016/j.cam.2003.08.032

• measure chain
• positive solution
• cone
• fixed point

In this paper, we consider the following dynamical system on a measure chain:
u(1)(DeltaDelta)(t) + f(1)(t,u(1)(sigma(t)), u(2)(sigma(t))) = 0, t is an element of [a, b],
u(2)(DeltaDelta)(t) + f(2)(t,u(1)(sigma(t)), u(2)(sigma(t))) = 0, t is an element of [a, b],
with the Sturm-Liouville boundary value conditions
alphau(i)(a) - betau(i)(Delta)(a) = 0, gammau(i)(sigma(b)) + deltau(i)(Delta)(sigma(b)) = 0 for i = 1, 2.
Some results are obtained for the existence of three positive solutions of the above problem by using Leggett-Williams fixed point theorem.

• 出版日期2004-1-15
• 单位兰州大学