An existence theorem for a nonlinear boundary value problem of fourth order (Q2367791)
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| Language | Label | Description | Also known as |
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| English | An existence theorem for a nonlinear boundary value problem of fourth order |
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An existence theorem for a nonlinear boundary value problem of fourth order (English)
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15 August 1993
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The paper deals with the existence of solutions for the following boundary value problem \(u^{(4)}=f(t,u,u',u'',u''')\), \(u'(0)=\varphi_ 1(u(0))\), \(u''(0)=\varphi_ 2(0))\), \(u'''(0)=\varphi_ 3(u(0))\), \(u'''(1)=\varphi_ 4(u(1),u'(1),u''(1))\). The author establishes his theorems by means of two unproved lemmas based on some results of \textit{I. T. Kiguradze} and \textit{N. R. Lezhava} [Methods of Function Theory in Differential Equations, 259-276 (1976; Zbl 0346.34008)] and \textit{M. Hukuhara} [Proc. Japan Acad. 29, 154-155 (1953; Zbl 0051.297)].
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nonlinear boundary value problems
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upper and lower solutions
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