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

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

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16) BERNARD A . FLEISHMAN and THOMAS J. MAHAB 50 To use a0 = sine /ax$,l estimate a + r cosg a w e e s t i m a t e x- and y - d e r i v a t i v e s for X Y’ S i n c e 0 < I$l 51 on aD and q1 i s harmonic i n D , we can - r p o i n t s i n D(E). / aY $ l 1 and If we can bound $ 1 as b e f o r e . o n aD, we can a l s o bound I axbll la and However, we know $1 on aD: $,(lA 1 /(ln = x2 s)f(uo(t))’ + $ I i n D(i ) . Y l y2 = 1 D For a l l p o i n t s i n 5 we h a v e , by Lemma A l , D D for any 6 E (0, 1/2).

H . , 7 3 These de 36me c y c l e , Universite de Paris-Sud, Orsay, 1977. T rlol Mercier C . [ll] Mercier C . L. Nirenberg m - - i n f r e e Boundary Problems, Annali Scuola Norm. Sup. ___ 1 The ma netoh drod namic a roach confinient c l o:ed m a g k n f -E ou r-4. - rl21 Mossino J . 4 t o the roblem of lasma i g E Z t h ~ c k E U R A T 0 M - Communication personnel l e . Etude de quelques roblemes non l i n e a i r e s d'un nouveau a a x s a n t en p h b s T a s m a s , Th6sFJniversXiEIF-Paris 3$-iEZF14n.

2. Chandra, J . , and Fleishman, B . A . , " E x i s t e n c e and comparison r e s u l t s f o r a c l a s s cf n o n l i n e a r boundary v a l u e problems," Annali d i Matematica Pura ed A p p l i c a t a , S e r i e IV-Tomo C I ( 1 9 7 4 ) , 247-261. 3. Fleishman, B . A . , and Mahar, T . J . , "Boundary v a l u e problems for a nonlinear d i f f e r e n t i a l equation with discontinuous nonlinearities," Math. B a l k . 3 ( 1 9 7 3 ) , 98-108.

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