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A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\). (English) Zbl 0708.34019
The authors consider the boundary value problem \((\phi_ p(u'))'+f(t,u)=0,\) \(u(0)=u(T)=0\), where \(f: [0,1]\times {\mathbb R}\to {\mathbb R}\) is continuous and \(\phi_ p(s)=| s|^{p-2}s,\) \(p>1\). The problem stated is investigated by means of the Leray-Schauder homotopy method.
Reviewer: V.G.Angelov

34B15 Nonlinear boundary value problems for ordinary differential equations
Full Text: DOI
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