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

In the paper, we shall prove that almost everywhere convergent bounded sequ ence in a Banach function space X is weakly convergent if and only if X and its dual space X* have the order continuous norms. Tt follows that almost everywhere convergent bounded sequence in L-P1 + L-P2 (1 < P-1, P-2 < infin ity) 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-Schrodinger equations. Copyright (C) 2000 John Wiley & Sons, Ltd.