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Additional resources for Equadiff IV: Proceedings, Prague, August 22–26, 1977

Example text

In this way naturally arose the question of the justification of the averaging method for the solution of boundary problems for ordinary differential equations. Do Bainov in 1964, and from 1970 on the authors of this survey achieved a number of new results. Some of these results are exposed in the present paper. I. ~. constructed for the Cauohy problem. 1) D~Yt~,~t,~)=Y~x~)+~Y,(x~,t)~ Y ~ ( x , ~ t ) ~ .... with i n i t i a l conation ~lLo)=~o ,~t~ol: ~= , where ×,~C ~ ~ > ~ ~ while ~ > 0 is a small parameter.

Rat. Mech. Anal. 5 (1969), 363-381. , and Sobolevskii, Structure of the set of solutions of an equation of parabolic type, Ukranian. Math. J. 16 (1964), 319-333. M. Nagumo, On principally linear elliptic differential equations of second order, Osaka, Math. J. 6 (1954), 207-229. V. Pao, Positive solutions of a nonlinear boundary value problem of parabolic type, J. Diff. Eqs. 22 (1976), 145-163. P. Puel, Existence comportement a l'infini et stabilite dans certaines problemes quasilineares elliptiques et paraboliques d'ordre 2, Ann.

Q is an infinite cyclic group whose elements, called central dispersions of Q, may be constructively described as follows: the value ~v(t) is the v th conjugate point with t lying ~o the right or to the left of t respectively for > 0 or ~ < 0 (~ integer). The functions ~_l and ~l are the generators of ~Q; in particular ~l is called the fundamental disper- sion of Q and there evidently holds: ~(t) = ~ ( t ) . The group ~Q is also called the center of Q; two equations with the same center are called concentric.

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