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Zbl 0920.34029
Cabada, Alberto; Pouso, Rodrigo L.
Existence results for the problem $(\varphi(u'))'= f(t,u,u')$ with nonlinear boundary conditions. (English)
[J] Nonlinear Anal., Theory Methods Appl. 35, No.2, A, 221-231 (1999). ISSN 0362-546X

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 $\bbfR$ onto $\bbfR$. The main tools are the method of lower and upper solutions, the Nagumo condition and the Schauder fixed point theorem.
[R.Precup (Cluj-Napoca)]

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE

Keywords: lower and upper solutions; Nagumo condition; Schauder fixed point theorem

Cited in: Zbl 0964.34016

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