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Solvability of a higher-order multi-point boundary value problem at a resonance. (English) Zbl 1249.34056
Sufficient conditions for the existence of solutions of a multi-point boundary value problem for an $$n$$-th order ordinary differential equation with a general right-hand side are given. The authors focus on the case when $$\text{dim ker }L=2$$, where $$L$$ is related to the linear equation $$Lx:=x^{(n)}(t)=0$$. Mawhin’s coincidence degree theory is applied for this aim. An illustrative example for a concrete third-order equation is supplied.
##### MSC:
 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations
##### Keywords:
multi-point BVP; higher-order ODE; resonance; degree arguments
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##### References:
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