A necessary and sufficient condition for the existence of positive solutions to a kind of singular three-point boundary value problem

作者：Zhao Junfang^*; Ge Weigao

来源：Nonlinear Analysis-Theory Methods & Applications, 2009, 71(9): 3973-3980.

DOI：10.1016/j.na.2009.02.067

• Singular
• Three-point boundary value problem
• Positive solutions
• Lower and upper solution
• Maximum principle

In this paper, we are concerned with the following three point boundary value problem
{u ''(t) + f(t, u(t)) = 0, 0 < t < 1, delta u'(0) - u(xi) = 0, u(1) = 0,
where delta >= xi, 0 < xi < 1, and the nonlinear term f may be singular at t = 1 or/and t = 0. A necessary and sufficient condition for the existence of C[0, 1] as well as C(1)[0, 1] positive solution 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 positive solutions are considered.

• 出版日期2009-11-1
• 单位北京理工大学