Multiple positive solutions for functional dynamic equations on time scales

作者：Wang, Da-Bin^*; Sun, Jian-Ping; Guan, Wen

来源：Computers & Mathematics with Applications, 2010, 59(4): 1433-1440.

DOI：10.1016/j.camwa.2009.12.019

• Time scale
• Functional dynamic equation
• Boundary value problem
• Positive solution
• Fixed point theorem

In this paper, we study the following functional dynamic equation on time scales:
{[Phi(u(Delta)(t))](del) + a(t)f(u(t), u(mu(t))) = 0, t is an element of (0, T)(T),
u(t) = phi(t), t is an element of [-r, 0)(T), u(0) - B-0(u(Delta)(0)) = 0, u(Delta)(T) = 0,
where Phi : R --> R is an increasing homeomorphism and a positive homomorphism and Phi(0) = 0. By using the well-known Leggett-Williams fixed point theorem, existence criteria for multiple positive solutions are established. An example is also given to illustrate the main results.

• 出版日期2010-2
• 单位兰州理工大学