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An application of Schauder’s fixed point theorem with respect to higher order BVPs. (English) Zbl 0895.34016
Summary: We provide conditions on the function \(f(t,u_{1},\cdots , u_{n-1})\) guaranteeing that the higher order boundary value problems \(u^{(n)}(t)+ f(t, u(t),u^{(1)}(t),\cdots ,u^{(n-2)}(t))=0\) for \(t\in(0,1)\) and \(n\geq 2\), \(u^{(i)}(0)=0\), \(0\leq i \leq n-3\), \(\alpha u^{(n-2)}(0)-\beta u^{(n-1)}(0)=0\), \(\gamma u^{(n-2)}(1)+\delta u^{(n-1)}(1)=0\) have at least one solution.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
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