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Existence of the solution of a boundary value problem for a system of first order ordinary differential equations with multipoint-functional boundary conditions

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Titel: Existence of the solution of a boundary value problem for a system of first order ordinary differential equations with multipoint-functional boundary conditions
Autoren: Korchak, B. E., Ponomarev, V. D.
Verlagsinformationen: Zinatne, Riga
Schlagwörter: Nonlinear boundary value problems for ordinary differential equations, Nonlocal and multipoint boundary value problems for ordinary differential equations
Beschreibung: Let \(I=[a,b]\), \(f_ i:I\times R^ n\to R\) be of Caratheodory type, and \(\phi_ i:R^ 2\to R\) continuous for \(1\leq i\leq n\). Consider the BVP (*) \(x_ i=f_ i\) \((t,x_ 1,...,x_ n)\), \(\phi_ i(x_ i(a_ i)\), \(x_ i(b_ i))=\phi_ i(x_ 1,...,x_ n)\), where \(\phi_ i's\) are continuous functionals on the space of absolutely continuous functions and \(a\leq a_ i\leq b_ i\leq b\). The authors give some (complex) conditions for the solvability in a generalized sense of BVP(*) both in the regular as well as the singular cases. The results extend some of the earlier ones by \textit{I. T. Kiguradze} and \textit{P. Puža} [Differ. Uravn. 12, 2139-2148 (1976; Zbl 0355.34009)] and \textit{B. Pužha} [Arch. Math. 13, 207-226 (1977; Zbl 0397.34028)].
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Zugangs-URL: https://zbmath.org/3877563
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  Data: Existence of the solution of a boundary value problem for a system of first order ordinary differential equations with multipoint-functional boundary conditions
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  Data: <searchLink fieldCode="AR" term="%22Korchak%2C+B%2E+E%2E%22">Korchak, B. E.</searchLink><br /><searchLink fieldCode="AR" term="%22Ponomarev%2C+V%2E+D%2E%22">Ponomarev, V. D.</searchLink>
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  Data: Zinatne, Riga
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  Data: <searchLink fieldCode="DE" term="%22Nonlinear+boundary+value+problems+for+ordinary+differential+equations%22">Nonlinear boundary value problems for ordinary differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlocal+and+multipoint+boundary+value+problems+for+ordinary+differential+equations%22">Nonlocal and multipoint boundary value problems for ordinary differential equations</searchLink>
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  Data: Let \(I=[a,b]\), \(f_ i:I\times R^ n\to R\) be of Caratheodory type, and \(\phi_ i:R^ 2\to R\) continuous for \(1\leq i\leq n\). Consider the BVP (*) \(x_ i=f_ i\) \((t,x_ 1,...,x_ n)\), \(\phi_ i(x_ i(a_ i)\), \(x_ i(b_ i))=\phi_ i(x_ 1,...,x_ n)\), where \(\phi_ i's\) are continuous functionals on the space of absolutely continuous functions and \(a\leq a_ i\leq b_ i\leq b\). The authors give some (complex) conditions for the solvability in a generalized sense of BVP(*) both in the regular as well as the singular cases. The results extend some of the earlier ones by \textit{I. T. Kiguradze} and \textit{P. Puža} [Differ. Uravn. 12, 2139-2148 (1976; Zbl 0355.34009)] and \textit{B. Pužha} [Arch. Math. 13, 207-226 (1977; Zbl 0397.34028)].
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      – SubjectFull: Nonlinear boundary value problems for ordinary differential equations
        Type: general
      – SubjectFull: Nonlocal and multipoint boundary value problems for ordinary differential equations
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      – TitleFull: Existence of the solution of a boundary value problem for a system of first order ordinary differential equations with multipoint-functional boundary conditions
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