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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
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