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

Schmitt, Klaus; Volkmann, Peter

doi:10.1090/S0002-9947-1976-0397110-5

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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Randwertaufgaben für gewöhnliche Differentialgleichungen

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