Get Differential Equations and Applications, Proceedings of the PDF

By Wiktor Eckhaus and Eduard M. de Jager (Eds.)

ISBN-10: 0444851852

ISBN-13: 9780444851857

Eckhaus e.W., Eduard M. de Jager. (eds.) Differential equations and functions (NH Pub. Co., 1978)(ISBN 0444851852)

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Extra resources for Differential Equations and Applications, Proceedings of the Third Scheveningen Conference on Differential Equations

Sample text

CourantHilbert [ 4 ] ) . 10) holds. 10) i s s a t i s f i e d . R. 1 or L2(a)n i s the norm in L 2( n) . Note t h a t the functional e i s unbounded in W : e ( v ) -+ t m for v = 6 v0 , v0 > 0 and 5 -+ t m , e ( v ) + -- f o r v 5 , 5 E R, 5 t . Therefore a c r i t i c a l point cannot be a minimum nor a maximum (see below). 1. -- results. For I > 0 and A > A~ given, Problem I1 possesses a t l e a s t one solution u = W The function u belongs to the Sobolev space W31a(a)' f o r a l l a 5 1 and to %2*q(x)f o r a l l rl satisfying .

Section 1 contains t h e d e r i v a t i o n o f the equations and t h e general f o r m u l a t i o n o f the problem. Section 2 gives t h e v a r i a t i o n a l f o r m u l a t i o n o f t h e problem and a statement o f the main r e s u l t s f o r a p a r t i c u l a r problem which is however s i g n i f i c a n t . Section 3 contains some i n d i c a t i o n s on t h e r e s u l t s obtained i n o t h e r cases, and f i n a l l y Section 4 i s devoted t o open problems : among these l e t us already mention - a s i n g u l a r p e r t u r b a t i o n problem - two problems o f b i f u r c a t i o n and existence o f m u l t i p l e s o l u t i o n s i n non standard s i t u a t i o n s : one o f these i s r e l a t e d t o t h e case where t h e p e r t u r b a t i o n i s not smooth (and i n some instances may not be s m a l l ) .

1091-lW4. R. Ac. , 0. H i l b e r t Methods o f Mathematical Physics, I n t e r s c i e n c e P u b l i s h e r s , New -953. [5] [6] - Oamlamian A . N. Expose au s e m i n a i r e d ' E q u a t i o n s aux d e r i v e e s p a r t i e l l e s non l i n e a i r e s , Orsay, 1977. C. Stevens A d i a b a t i c e v o l u t i o n of lasrna e u i l i b r i u m , Proc. Nat. Ac. Sc. 72, N O 10 , l h . h R. TEMAM 38 3 - [7] Guillope C . [8] Hartman P . , A. Wintner On the local behavior of solut'ions of non a r a b o l i c a r t i a l dTfEFeE5T equationsyher.

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Differential Equations and Applications, Proceedings of the Third Scheveningen Conference on Differential Equations by Wiktor Eckhaus and Eduard M. de Jager (Eds.)


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