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On weakly convergent sequences in Banach function spaces and the initial‐boundary value problems for non‐linear Klein–Gordon–Schrödinger equations
Author(s) -
Baoxiang Wang
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/1099-1476(200012)23:18<1655::aid-mma179>3.0.co;2-2
Subject(s) - mathematics , banach space , bounded function , almost everywhere , sequence (biology) , initial value problem , boundary value problem , mathematical analysis , limit of a sequence , pure mathematics , function space , genetics , limit (mathematics) , biology
In the paper, we shall prove that almost everywhere convergent bounded sequence in a Banach function space X is weakly convergent if and only if X and its dual space X * have the order continuous norms. It follows that almost everywhere convergent bounded sequence in L p 1+ L p 2(1< p 1 , p 2 <∞) is weakly convergent. On the basis of this property, we get the global existence of weak solutions for the initial–boundary value problem of non‐linear Klein–Gordon–Schrödinger equations. Copyright © 2000 John Wiley & Sons, Ltd.