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I n view of t h e e m p i r i c a l f a c t t h a t t h e number of s o l u t i o n s c a n change w i t h c h a n g e s of D (cf. $ 6 ) , what i s t h e t y p i c a l form of t h e b i f u r c a t i o n s from which t h e new solutions arise? What p r o p e r t i e s of such b i f u r c a t i o n s and o f o t h e r s t e a d y - f l o w phenomena a r e s t r u c t u r a-~ l l y s t_a_b le, so that t h e y may b e o b s e r v a b l e i n p r a c t i c e ? Adopting t h e p r a c t i c a l s t a n d p o i n t a l r e a d y proposed, we may c l a s s i f y p r o p e r t i e s as t y p i c a l when t h e weight a v a i l a b l e evidence and i n t u i t i v e - - mathematical, suggests that of such a s i t i s , e m p i r i c a l t h e s e p r o p e r t i e s a r e predominant and t h e r e i s no o b v i o u s r e a s o n t o t h e c o n t r a r y .

Magnetogasdynamics and Plasma Dynamics, Springer, 1962. H. Wilcox, Wave operators and asymptotic solutions o f wave propagation problems of classical physics, Arch. Rat. Mech. Anal. 22 (1966) PP. 37-78. H. Wilcox, Measurable eigenvectors f o r Hermitian matrix-valued polynomials, J. Ma h. Anal. Appl. 12-19. M. A. B. Baillon John M . Department of Mathematics Dept. de Math6matiques &ole Chadam*f Pontificia Universidade Polytechnique Cat6lica do Rio de Janeiro Paris, France Rio de Janeiro, Brasil Introduction.

O n Coupled Klein-Gordonto appear. Non-linear Semi-groups, Ann. Math. 7 7 , 339 (1963). C 73 Grisvard P, - Contribution i n Proceedings o f Evolution Equation Seminar, Nice, France 1974-5. , Cazenave, T. and Figueira, M. R. Acad. Sci [ 91 . , Cazenave, T. and Figueira, M. - Equations de Schradinger Non-lin&aire, 11, to appear CR. Acad. Sci. [lo] Reed, M. and Simon, B. - Methods o f Modern Mathematical Physics 11, Academic Press, 1975. M. de La Penha, L . A . B. BENJAMIN Fluid Mechanics Research Institute University of Essex, England 1.

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