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This article is cited in 5 scientific papers (total in 5 papers)
Monotonicity in the theory of almost periodic solutions of nonlinear operator equations
V. V. Zhikov
Abstract:
In a Banach space with a strictly convex norm we consider a nonlinear equation $u'+A(t)u=0$ of general form. Suppose that a “monotonicity” condition is satisfied: for any two solutions $u_1(t)$ and $u_2(t)$ the function $g(t)=\|u_1(t)-u_2(t)\|$ is nonincreasing with respect to $t$; suppose $A(t)$ is almost periodic (in some sense) with respect to $t$.
The basic theorem reads as follows: given strong (weak) continuity of the solutions with respect to the initial conditions and the coefficients, there exists at least one almost periodic solution if there exists a compact (weakly compact) solution on $t\geqslant0$.
Bibliography: 26 titles.
Received: 21.06.1972
Citation:
V. V. Zhikov, “Monotonicity in the theory of almost periodic solutions of nonlinear operator equations”, Mat. Sb. (N.S.), 90(132):2 (1973), 214–228; Math. USSR-Sb., 19:2 (1973), 209–223
Linking options:
https://www.mathnet.ru/eng/sm3007https://doi.org/10.1070/SM1973v019n02ABEH001746 https://www.mathnet.ru/eng/sm/v132/i2/p214
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Abstract page: | 573 | Russian version PDF: | 186 | English version PDF: | 4 | References: | 43 |
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