Boundary Value Problems for Second Order Differential Equations in Convex Subsets of a Banach Space
Year: 1976
Type: article
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 $u:[0,1] \to C$.
Authors: Klaus Schmitt, Peter Volkmann
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2032831011