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By Nakamoto A., Sasanuma N.

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M. A. Krasnosel'sky and E. A. Lifschitz, "Affinity principles for differential equations with unbounded operators in a Banach space," Funk. Anal. , 2, No. 4, 58-62 (1968). 21. M. A. Krasnosel'sky and E. A. Lifschitz, "On certain general tests of existence of periodic oscillations in nonlinear systems," Avtomat. , No. 9, 12-15 (1973). 22. M. A. Krasnosel'sky and A. I. Perov, "On one principle of existence of bounded, periodic, and almost periodic solutions of systems of ordinary differential equations," Dokl.

Dementyeva, "On an affinity theorem," In: Applied Methods of Functional Analysis [in Russian], Voronezh State University, Voronezh (1985), pp. 29-33. 4. N. A. Bobylev, A. M. Krasnosel'sky, and M. A. Krasnosel'sky, "The stability of periodic oscillations and the possibility of their construction by the harmonic balance method," A vtomat. , No. 7, 179-181 (1989). 11 0 0 N. A. Bobylev and M. A. Krasnosel'sky, "The functionalization of a parameter and the affinity theorem for autonomous systems," Differents.

3. T h e affinity principles for elliptic equations. boundary. We shall consider the Dirichlet problem 0a). 22) = w(,). o. 2:3 / "~z; F aCxluCz) i=1 of the second order with smooth coefficients aij(z), ai(z), a(z) (z e fl) such that the estimate N N i=1 i,j=l is valid for a certain v > 0. 22) has only a zero solution. 24) u = Aow + Alv, 9 where A0: Eo * El, A1 : E ~ E1 are linear bounded operators. 22) are, for instance, the triples {C(fl), C(Of~), C'(~)}, {C~(~), C"(Ofi), C2+"(~)}, where C~(fl), C"(Ofl), C2+~('fl) are HSlder spaces.

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