Uniqueness and parameter dependence of solutions of second-order boundary value problems

作者：Kong Lingju^*; Kong Qingkai

来源：Applied Mathematics Letters, 2009, 22(11): 1633-1638.

DOI：10.1016/j.aml.2009.05.009

• Positive solutions
• Boundary value problems
• Uniqueness
• Dependence on parameters
• Normal solid cones

We consider the boundary value problem with nonhomogeneous multi-point boundary condition
u '' + a(t)f(u) = 0, t is an element of (0, 1),
u(0) = Sigma(m)(i=1) a(i)u(t(i)) + lambda, u(1) = Sigma(m)(i=1) b(i)u(t(i)) + mu.
A sufficient condition is obtained for the existence and uniqueness of a positive solution. The dependence of the solution on the parameters lambda and mu is also studied. Our work complements some results in the literature, especially those in our earlier papers [L Kong, Q. Kong, Second-order boundary value problems with non homogeneous boundary conditions I, Math. Nachr. 278 (2005) 173-193; L Kong, Q. Kong, Second-order boundary value problems with nonhomogeneous boundary conditions II, J. Math. Anal. Appl. 330 (2007) 1393-1411].

• 出版日期2009-11