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Oscillation of nonlinear systems of matrix differential equations

Name: Oscillation of nonlinear systems of matrix differential equations
Creator: Kartsatos, A.G.
Keywords: 13. Climate action, Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Sep 1971 Greece English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 30, pages 97-101 (issn: 0002-9939, eissn: 1088-6826,

Authors: Kartsatos, A.G.;

doi: 10.1090/s0002-9939-1971-0280798-8 , 10.2307/2038230

Oscillation of nonlinear systems of matrix differential equations

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Abstract

For systems of matrix equations of the form \[ U ′ = A ( t , U , V ) V , V ′ = − B ( t , U , V ) U’ = A(t,U,V)V,\quad V’ = - B(t,U,V) \] it is shown here that the oscillation problem can be reduced to the corresponding problem of “associated” (in some sense) scalar equations for which there exist numerous results. Furthermore, it is also shown that many of the existing results concerning the equation \[ ( A ( t ) U ′ ) ′ + B ( t , U , U ′ ) U = 0 (A(t)U’)’ + B(t,U,U’)U = 0 \] can be considerably improved by application of the above method.

Country

Greece

Related Organizations

National and Kapodistrian University of Athens
Greece

Keywords

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

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