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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Boundary value problems for second order differential equations in convex subsets of a Banach space
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by Klaus Schmitt and Peter Volkmann PDF
Trans. Amer. Math. Soc. 218 (1976), 397-405 Request permission

Abstract:

Let E be a real Banach space, C a closed, convex subset of E and $f:[0,1] \times E \times E \to E$ be continuous. Let ${u_0},{u_1} \in C$ and consider the boundary value problem \begin{equation}\tag {$\ast $} u'' = f(t,u,u’),\quad u(0) = {u_0},\quad u(1) = {u_1}.\end{equation} We establish sufficient conditions in order that $(\ast )$ have a solution $u:[0,1] \to C$.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 218 (1976), 397-405
  • MSC: Primary 34G05
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0397110-5
  • MathSciNet review: 0397110