## 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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### References:

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