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A new upper and lower solutions approach for second order problems with nonlinear boundary conditions. (English) Zbl 1098.34520
Consider the nonlinear boundary value problem \begin{aligned} & u''=f(t,u),\quad 0<t<T,\\ & g(u(0),u(T),u'(0))=0,\\ & h(u(0),u(T),u'(0))=0,\end{aligned} \tag{*} where $$f,g$$ and $$h$$ are continuous functions. The authors give a new definition of lower and upper solutions for (*) and establish the existence of a solution of (*).

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