Castro B. Alfonso (auth.), Djairo Guedes de Figueiredo,'s Differential Equations: Proceedings of the 1st Latin PDF
By Castro B. Alfonso (auth.), Djairo Guedes de Figueiredo, Chaim Samuel Hönig (eds.)
Read Online or Download Differential Equations: Proceedings of the 1st Latin American School of Differential Equations, Held at São Paulo, Brazil, June 29–July 17, 1981 PDF
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Extra info for Differential Equations: Proceedings of the 1st Latin American School of Differential Equations, Held at São Paulo, Brazil, June 29–July 17, 1981
I n d i a n a U n i v . Math. J. 20 (1971) 983-996. ~] A m b r o s e t t i , A. E x i s t e n z a de I n f i n i t e Soluzione N o n l i n e a r i in Assenza di Parametro. A t t i L i n c e i 52 (1972) 660-667.  ~ ~] R a b i n o w i t z , P. Some Minimax Theorems and A p p l i c a t i o n s to N o n l i n e a r P a r t i a l D i f f . E q u a t i o n s . In " N o n l i n e a r A n a l y s i s " Academic Press (1978) 161-177. ~] ~  A m b r o s e t t i , A. & M a n c i n i , G. Theorems of E x i s t e n c e and Multiplicity for Nonlinear Elliptic Problems w i t h N o n i n v e r t i b l e L i n e a r P a r t .
For (x)] x o G Q, we c a n n o t the above bounds on sharp. f (14) fo(X)] fo < sup f ~ , positive Observe t h a t then fo(X)]. f~(Xo) for x o G Q, 0 < ~ <~l(1)/[sup ~ O, ~ > ~l(1)/[inf in by the p r e s e n t method. for solution ~ all < +~ then problem existence (Xo) > 0 in for 0 < fo(X) anything f has a p o s i t i v e 0 < fo(X) positive d) m +~ we e s t a b l i s h involving assumptions some on g we a l w a y s assume (15) It is the functions s ---~ g ( x , easy to see t h a t concave i n Lemma 2 .
L=I ~i¢ i (T@, d#) : (II). e. 4 be any system of the subspace g e n e r a t e d i n such a way t h a t and (13) Fn_l]. we see by P r o p o s i t i o n hI . . . and and n o r m a l i z e x l side of hand l e t H with -n = I, ¢I' .... ]. l=I 2 ~i : I . (@, h i ) II~11 Now = 0 = 1 > ~n" which implies (14) sup [ ( T x , and consequently x):llxtl : l, x- Fn_l] > ~n' V Fn_ 1 . D. 8. For each result. n positive sup (Tx, dimension. This x) has to situation 40 (15) Xn : sup i n f Fn where the dimension supremum i s n.
Differential Equations: Proceedings of the 1st Latin American School of Differential Equations, Held at São Paulo, Brazil, June 29–July 17, 1981 by Castro B. Alfonso (auth.), Djairo Guedes de Figueiredo, Chaim Samuel Hönig (eds.)