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Existence results for the problem \((\varphi(u'))'= f(t,u,u')\) with nonlinear boundary conditions. (English) Zbl 0920.34029
The authors prove an existence result for problems of the form \[ (\phi(u'))'= f(t,u,u')\text{ a.e. }t\in [a,b],\;g(u(a), u'(a), u'(b))= 0,\;h(u(a))= u(b), \] where \(\phi\) is continuous and increasing from \(\mathbb{R}\) onto \(\mathbb{R}\). The main tools are the method of lower and upper solutions, the Nagumo condition and the Schauder fixed point theorem.

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