Hale, J.K., Ordinary Di#erential Equations, Wiley--Interscience, New York, 1969. Home/Search Document Not in Database Summary Related Articles Check |
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Conformal Properties of Harmonic Spinors and Lightlike Geodesics.. - Witt (2001) (Correct)
....Lorentzian surface is complete. 7 We recall that a vector eld K is called conformal if LK g = g for a smooth function (L denotes the Lie derivative) 2.2. 3 For the global behaviour of the null lines, the Poincar e Bendixson theory for ordinary di erential equations on the torus (see e.g. [Ha69] and references quoted there) asserts that a null line is either: dense or a closed curve homeomorphic to S which cannot be contracted to a point, or asymptotic of a closed null line of the same type A tool to decide which case applies for a given isotropic ow is given by the ....
J.Hale. Ordinary di erential equations. Wiley-Interscience, New York, 1969.
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....the multi indices of order #I n, are the coecients of L. 3. Wronskians and Stabilization. The most basic necessary and sucient condition for the linear independence of solutions to a homogeneous linear scalar ordinary di erential equation is the nonvanishing of their Wronskian determinant, cf. [20]. Many of our results will rely on a signi cant multidimensional generalization of this classical Wronskian lemma, which can be applied to any collection of analytic functions. We refer to [37] for details on the following de nitions and results, including extensions to both smooth and ....
Hale, J.K., Ordinary Di erential Equations, Wiley{Interscience, New York, 1969.
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....# , since T , 1# =1 X T # , 1 t,T , 1# . Therefore, we wish to obtain the solution of (11) 4 The Fundamental Matrix Solution If S(t) is a matrix satisfying certain conditions the matrix di#erential equation . # (t) S(t)#(t) #(0) I has a unique solution (see [5], for example) defined for 0 t #. Here I is the n n matrix. For each t 0, the matrix #(t) is nonsingular. Suppose further we have the n dimensional vector #,nn matrix S(t) and a deterministic equation . # (t) S(t)#, #(0) #. 12) 7 In terms of the #, the solution of the deterministic ....
J. Hale. Ordinary Di#erential Equations. J. Wiley & Sons/Interscience, New York, 1969
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Hale, J.K., Ordinary Di#erential Equations, Wiley--Interscience, New York, 1969.
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Hale J. [1969]: Ordinary Dierential Equations, Wiley, NY
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