A necessary and sufficient condition for the existence of positive solutions to singular sublinear three-point boundary value problems

作者：Du Xinsheng^*; Zhao Zengqin

来源：Applied Mathematics and Computation, 2007, 186(1): 404-413.

DOI：10.1016/j.amc.2006.07.120

• second-order singular three-point boundary value problems
• positive solution
• lower and upper solution
• maximum principle

This paper investigates the existence of positive solutions for second-order singular sublinear three point boundary value problems. A necessary and sufficient condition for the existence of C[0, 1] as well as C-1[0, 1] positive solutions is given by constructing lower and upper solutions and with the maximal theorem. Also, the uniqueness, iterative methods, convergence rate and computational methods of the C1 [0, 1] positive solutions are studied. Our nonlinear term may be singular at t = 0 and/or t = 1.

• 出版日期2007-3-1
• 单位曲阜师范大学