Second order singular boundary value problems with integral boundary conditions

作者：Kong Lingju^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 72(5): 2628-2638.

DOI：10.1016/j.na.2009.11.010

• Positive solutions
• Singular boundary value problem
• Integral boundary condition
• Existence
• Uniqueness
• Dependence
• Mixed monotone operator

we study the second order singular boundary value problem
u '' + lambda f(t, u) = 0, t is an element of (0, 1),
u(0) = integral(1)(0) u(s)d xi(s), u(1) = integral(1)(0) u(s)d eta(s).
Sufficient conditions are obtained for the existence and uniqueness of positive solutions. The dependence of positive solutions on the parameter lambda is also studied. Moreover, application of our theory to a special problem is discussed.To prove our theorem, we utilize some results from the mixed monotone operator theory.

• 出版日期2010-3-1