MULTIPLE POSITIVE SOLUTIONS FOR SEMIPOSITONE (n, p)-TYPE BOUNDARY VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

作者：Yuan Chengjun^*

来源：Analysis and Applications, 2011, 9(1): 97-112.

DOI：10.1142/S0219530511001753

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

In this paper, we consider the (n, p)-type boundary value problem of nonlinear fractional differential equation
D(0)(+)(alpha) u(t) + lambda f(t, u(t)) = 0, 0 < t < 1
u((j))(0) = 0, 0 <= j <= n - 2,
u((p))(1) = 0,
where lambda is a parameter, alpha is an element of (n - 1, n] is a real number and n >= 3, 1 <= p <= alpha- 1 is fixed and integer, D(0+)(alpha) is the Riemann-Liouville's fractional derivative, and f is continuous and semipositone. We derive an interval of lambda such that any lambda lying in this interval, the semipositone boundary value problem has multiple positive solutions.

• 出版日期2011-1
• 单位哈尔滨学院