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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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##### References:
  Cabada, A.; Pouso, R.L., Existence result for the problem(φ(u′))′=f(t,u,u′) with periodic and Neumann boundary conditions, Nonlinear anal. T.M.A., 30, 1733-1742, (1997) · Zbl 0896.34016  DeCoster, C., Pairs of positive solutions for the one-dimensionalp-Laplacian, Nonlinear anal. T.M.A., 23, 669-681, (1994) · Zbl 0813.34021  Fabry, Ch.; Habets, P., Upper and lower solutions for second-order boundary value problems with nonlinear boundary conditions, Nonlinear anal. T.M.A., 10, 985-1007, (1986) · Zbl 0612.34015  Lloyd, N.G., Degree theory, (1978), Cambridge University Press Cambridge · Zbl 0367.47001  McShane, E.J., Integration, (1967), Princeton University Press Princeton · Zbl 0146.07202  O’Regan, D., Some general principles and results for(φ(y′))′=qf(t,y,y′),0
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