Download Equadiff 9: Conference on Differential Equations and their by Z. Dosla, J. Kuben, J.Vosmansky PDF

By Z. Dosla, J. Kuben, J.Vosmansky

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Extra info for Equadiff 9: Conference on Differential Equations and their Applications : Proceedings

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E. for t ∈ [0, µ−2 ϕ1 (1)]. mar ). We are bound to give the only remark. Remark 3. Coefficients αrjjk (x), j = 2, p − 1 derived from the simple elements λj (x) can be defined by scalar linear differential equations of the first order. mar ) the following changes. Coefficients αrjjk (x) (j = p, n) derived from multiple elements of the spectrum can be determined by the system of (n − p + 1) differential equations. 50 6 V. N. Bobochko and I. I. mar ) and so on. Each of those solutions contains 2n arbitrary constants which were obtained by integrations of differential equations and systems of differential equations with respect to unknown functions Vrlk (x), αrjjk (x), j = 2, n; k = 1, 2.

1996, t. 48, No 2, 147–160. [4] Bobochko V. , Asymptotics solutions of a system differential equations with a multiple turning point, Diff. Equat. 1996, t. 32, No 9, 1153–1155. [5] Lomov S. , Introduction to the general theory of singular perturbations, Moscow, Nauka, 1981, 400 p. [6] Gantmacher F. , Theory of matrices, Moscow, 1953, 492 p. [7] Olver F. W. , Asymptotic and special functions, Moscow, Nauka, 1990, 528 p. EQUADIFF 9 CD ROM, Brno 1997 Masaryk University PAPERS pp. hu Abstract. The existence and uniqueness of symmetric solutions to the boundary value problem of nonlinear partial differential equations are established.

I. Markush where ε → +0, x ∈ I = [0, 1], m = 0, 1, µ= √ 3 ε. Here A denotes a linear operator on Rn , αm and Wm are given vectors, Ek (k = 1, 2) — diagonal matrices of the nth order of the form E1 = diag{1, 0, . . , 0}, E2 = diag{0, 1, . . , 1), h(x) — given vector-function, W (x, ε) — a sought vectorfunction. mar ) under the following conditions: 1◦ A(x), h(x) ∈ C ∞ [I] 2◦ Spectrum of the degenerate operator A is real and fulfills the following condition 0 ≤ λ1 (x) ≡ xλ1 (x) < λ2 (x) < · · · < λp.

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