Multiple positive solutions to singular positone and semipositone Dirichlet-type boundary value problems of nonlinear fractional differential equations

作者：Xu, Xiaojie^*; Jiang, Daqing; Yuan, Chengjun

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(16): 5685-5696.

DOI：10.1016/j.na.2011.05.055

• Multiple positive solutions
• Singular fractional differential equation
• Leray-Schauder nonlinear alternative
• Boundary value problem

In this paper, we establish the existence of multiple positive solutions to positone and semipositone Dirichlet-type boundary value problems of the nonlinear fractional differential equation:
D(0+)(alpha) u(t) + f(t, u(t)) = 0, 0 < t < 1,
u(0) = u(1) = 0
by using the Leray-Schauder nonlinear alternative and a fixed-point theorem on cones, where 1 < alpha < 2 is a real number and D(0+)(alpha) is the standard Riemann-Liouville derivative. Here our nonlinearity f may be singular at u = 0.

• 出版日期2011-11
• 单位哈尔滨学院; 中国石油大学（华东）; 东北师范大学