Solutions of multi-point boundary value problems of the second order. (English) Zbl 1140.34309
Ladde, G. S. (ed.) et al., Proceedings of neural, parallel, and scientific computations. Vol. 3. Papers based on the presentations at the 3rd international conference, Atlanta, GA, USA, August 09–12, 2006. Atlanta, GA: Dynamic Publishers (ISBN 1-890888-02-8/pbk). 68-72 (2006).
Summary: Consider the boundary value problem consisting of the equation
\[ u''+f(t,u)=0,\quad t\in (0,1), \]
and the boundary condition
\[ u(0)=\sum^m_{i=1} a_iu(t_i),\quad u(1)=\sum^m_{i=1} b_iu(t_i), \]
where \(m\geq 1\) is an integer, \(t_i\in(0,1)\), and \(a_i,b_i\in [0,\infty)\) for \(i=1,\dots,m\), and \(f:(0,1)\times\mathbb R\to\mathbb R\) is continuous and nondecreasing in \(x\).
We prove several existence results which extend some known work in the literature.
For the entire collection see [Zbl 1130.68011].
\[ u''+f(t,u)=0,\quad t\in (0,1), \]
and the boundary condition
\[ u(0)=\sum^m_{i=1} a_iu(t_i),\quad u(1)=\sum^m_{i=1} b_iu(t_i), \]
where \(m\geq 1\) is an integer, \(t_i\in(0,1)\), and \(a_i,b_i\in [0,\infty)\) for \(i=1,\dots,m\), and \(f:(0,1)\times\mathbb R\to\mathbb R\) is continuous and nondecreasing in \(x\).
We prove several existence results which extend some known work in the literature.
For the entire collection see [Zbl 1130.68011].
MSC:
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
