On weakly convergent sequences in Banach function spaces and the initial-boundary value problems for non-linear Klein–Gordon–Schrödinger equations

✍ Scribed by Wang Baoxiang

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 123 KB
• Volume: 23
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/1099-1476(200012)23:18<1655::aid-mma179>3.0.co;2-2

✦ Synopsis

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 ¸N #¸N (1(p , p (R) 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}Schro K dinger equations.