Rendiconti del Circolo Matematico di Palermo

, Volume 31, Issue 3, pp 305–320 | Cite as

Nonlinear second order boundary value problems: Continuous dependence and periodic boundary conditions

  • John V. Baxley
Article
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Keywords

Unique Solution Maximum Principle Periodic Boundary Condition Continuous Dependence Positive Maximum 
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Zusammenfassung

Zwei-punkt Randwertaufgaben für die Differentialgleichung (*)y″=f(x,y,y′),a≤x≤b, sind betrachtet. Ziemlich gewöhnliche hinreichende Bedingungen sind gegeben für die Existenz und Einzigkeit einer Lösung Φ(x,α,β) der Gleichung (*) und die Randbedingungeng(y(a), y′(a))=α, h(y(b), y′(b))=β, und für die stegige Abhängigkeit der beiden Φ′(x, α, β) von (x, α, β). Diese Ergebnisse haben dann zur Folge Existenz- und Einzig- keitsätze für die verallgemeinerte periodische Randwertaufgabe, die aus der Gleichung (*) und den Randbedingungeny(a)=y(b)+G (y′(a), y(b), H(y′(a), y′(b))=0 bestehen.

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References

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Copyright information

© Springer 1982

Authors and Affiliations

  • John V. Baxley
    • 1
  1. 1.Department of MathematicsWake Forest UniversityWinston-Salem

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