Multiple positive solutions for (n-1, 1)-type semipositone conjugate boundary value problems for coupled systems of nonlinear fractional differential equations

作者：Yuan Chengjun^*

来源：Electronic Journal of Qualitative Theory of Differential Equations, 2011, (13): 1-12.

• Riemann-Liouville's fractional derivative
• fractional differential equation
• boundary value problem
• positive solution
• fractional Green's function
• fixed-point theorem

In this paper, we consider (n-1, 1)-type conjugate boundary value problem for coupled systems of the nonlinear fractional differential equation
{D(0+)(alpha) u + lambda f(t, v) = 0, 0 < t < 1, lambda > 0,
D(0+)(alpha) v + lambda g(t, u) = 0,
u((i))(0) = v((i))(0) = 0, 0 <= i <= n-2,
u(1) =v(1) = 0,
where lambda is a parameter, alpha is an element of (n - 1, n] is a real number and n >= 3, and D(0+)(alpha) is the Riemann- Liouville's fractional derivative, and f, g are continuous and semipositone. We give properties of Green's function of the boundary value problem, and derive an interval on lambda such that for any lambda lying in this interval, the semipositone boundary value problem has multiple positive solutions.

• 出版日期2011
• 单位哈尔滨学院