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Transactions of the American Mathematical Society

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

 
 

 

Boundary value problems for second order differential equations in convex subsets of a Banach space


Authors: Klaus Schmitt and Peter Volkmann
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
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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

$\displaystyle u'' = f(t,u,u'),\quad u(0) = {u_0},\quad u(1) = {u_1}.$ ($ \ast$)

We establish sufficient conditions in order that $ (\ast)$ have a solution $ u:[0,1] \to C$.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0397110-5
Keywords: Boundary value problems, second order differential equations in Banach spaces
Article copyright: © Copyright 1976 American Mathematical Society

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