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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 \(f\).

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
Full Text: DOI
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