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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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