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Zeitschrift für Analysis und ihre Anwendungen


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Volume 7, Issue 4, 1988, pp. 337–346
DOI: 10.4171/ZAA/310

Published online: 1988-08-31

Solvability of Boundary Value Problems for the Inclusion $u_{tt} - u_{zz} \in g(t, x, u)$ via the Theory of Multi-Valued A-Proper Maps

Tomasz Kaszynski[1] and Wieslaw Krawcewicz[2]

(1) Université de Sherbrooke, Sherbrooke (Québec), Canada
(2) University of Alberta, Edmonton, Canada

The existence of a coincidence point $x$ for the inclusion $$Lx \in \Gamma(x)$$ is studied where $L: D(L) \subset E \to F$ is a linear hyperbolic operator and $\Gamma : E \to 2^F$ is a convex-valued map. It is shown that any such monotone demi-continuous map $\Gamma$ is weakly $A$-proper. Some existence theorems for ($\ast$) are established and the reults are applicated to a boundary value problem for the inclusion $u_{tt} - u_{zz} \in g(t, x, u)$.

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Kaszynski Tomasz, Krawcewicz Wieslaw: Solvability of Boundary Value Problems for the Inclusion $u_{tt} - u_{zz} \in g(t, x, u)$ via the Theory of Multi-Valued A-Proper Maps. Z. Anal. Anwend. 7 (1988), 337-346. doi: 10.4171/ZAA/310