## Existence results for $$m$$-point boundary value problems.(English)Zbl 0877.34019

The paper deals with existence and uniqueness of solutions of a boundary value problem of the form $x''(t)= f(t,x(t),x'(t))+ e(t),\quad 0<t<1,\quad x(0)=0\quad\text{and }x'(1)= \sum^{m-2}_{i=1} a_ix'(\xi_i),$ where $$0<\xi_i<\cdots<\xi_{m- 2}<1$$, the coefficients $$a_i$$ have the same sign, $$\sum a_i=1$$. Some existence results are obtained by using the Leray-Schauder continuation theorem.

### MSC:

 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34G20 Nonlinear differential equations in abstract spaces 34B15 Nonlinear boundary value problems for ordinary differential equations