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

del Pino, Manuel A.; Elgueta, Manuel; Manásevich, Raúl

J. Differ. Equations 80, No. 1, 1-13 (1989).

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

MSC:

34B15

Nonlinear boundary value problems for ordinary differential equations

Keywords:

Leray-Schauder homotopy method

References:

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