Multidimensional analog of the two-dimensional perron effect of sign change of characteristic exponents for infinitely differentiable differential systems |
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Authors: | N A Izobov S K Korovin |
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Institution: | 1. Institute of Mathematics, National Academy of Sciences, Minsk, Belarus 2. Moscow State University, Moscow, Russia
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Abstract: | We obtain a general n-dimensional analog of the two-dimensional (partial) Perron effect of sign change of all arbitrarily prescribed negative characteristic exponents of an n-dimensional differential system of the linear approximation with infinitely differentiable bounded coefficients to the positive sign for the characteristic exponents of all nontrivial solutions of a nonlinear n-dimensional differential system with infinitely differentiable perturbations of arbitrary order m > 1 of smallness in a neighborhood of the origin and growth outside it. These positive exponents take n values distributed over n arbitrarily prescribed disjoint intervals and are realized on solutions issuing from nested subspaces R 1 ? R 2 ? ... ? R n . |
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