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Page 564
E 19 Find the most general solution of the differential equation y ' Ty where T is the matrix of Exercise 5 . The next ten exercises refer to the stability theory of systems of n linear homogeneous differential equations , dy ( t ) / dt ...
E 19 Find the most general solution of the differential equation y ' Ty where T is the matrix of Exercise 5 . The next ten exercises refer to the stability theory of systems of n linear homogeneous differential equations , dy ( t ) / dt ...
Page 610
have unique solutions for any y in X or y * in X * if and only if the homogeneous equations ( H ) ( 11 - T ) x = 0 ... Furthermore if one of the homogeneous equations has a non - zero solution , then they both have the same finite ...
have unique solutions for any y in X or y * in X * if and only if the homogeneous equations ( H ) ( 11 - T ) x = 0 ... Furthermore if one of the homogeneous equations has a non - zero solution , then they both have the same finite ...
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The Ly - solutions of linear differential equations of second order . Duke Math . J. 14 , 323–326 ( 1947 ) . 4. Unrestricted solution fields of almost separable differential equations . Trans . Amer . Math . Soc .
The Ly - solutions of linear differential equations of second order . Duke Math . J. 14 , 323–326 ( 1947 ) . 4. Unrestricted solution fields of almost separable differential equations . Trans . Amer . Math . Soc .
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm operator positive measure problem Proc Proof properties proved respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero