Solvability of a multi-point boundary value problem at resonance.(English)Zbl 0843.34023

The Leray-Schauder continuation method is used to find sufficient conditions which imply the existence of at least one solution for multi-point boundary value problems of the form $x'' (t) = f \bigl( t,x(t), x'(t) \bigr) + e(t),\;x(0) = 0,\;x(1) = {1 \over k} \sum^k_{i = 1} a_i x(\eta_i).$ The assumptions involve growth and sign conditions upon $$f$$.

MSC:

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

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