. . . "instability, general n-dimensional system of ordinary differential equations with quadratic right-hand sides, the zero solution, cone, Chetaevs method"@en . . "RIV/00216305:26220/11:PU91522" . . . . "2011" . . "Dibl\u00EDk, Josef" . "Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone" . . "P(GAP201/10/1032), P(GAP201/11/0768), Z(MSM0021630503), Z(MSM0021630519)" . . . "23"^^ . "FK - Falklandsk\u00E9 ostrovy" . . "RIV/00216305:26220/11:PU91522!RIV12-GA0-26220___" . . . . "[EF7D7EB9B061]" . "Khusainov, Denys" . "4"^^ . . "The present investigation deals with global instability of a general n-dimensional system of ordinary differential equations with quadratic right-hand sides. The global instability of the zero solution in a given cone is proved by Chetaevs method, assuming that the matrix of linear terms has a simple positive eigenvalue and the remaining eigenvalues have negative real parts. The sufficient conditions for global instability obtained are formulated by inequalities involving norms and eigenvalues of auxiliary matrices. In the proof, a result is used on the positivity of a general third-degree polynomial in two variables to estimate the sign of the full derivative of an appropriate function in a cone." . . "Svoboda, Zden\u011Bk" . "\u0160marda, Zden\u011Bk" . "The present investigation deals with global instability of a general n-dimensional system of ordinary differential equations with quadratic right-hand sides. The global instability of the zero solution in a given cone is proved by Chetaevs method, assuming that the matrix of linear terms has a simple positive eigenvalue and the remaining eigenvalues have negative real parts. The sufficient conditions for global instability obtained are formulated by inequalities involving norms and eigenvalues of auxiliary matrices. In the proof, a result is used on the positivity of a general third-degree polynomial in two variables to estimate the sign of the full derivative of an appropriate function in a cone."@en . "26220" . . . . "Khusainov, Denys" . "4"^^ . "Abstract and Applied Analysis" . "205052" . "Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone" . "Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone"@en . "Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone"@en . . . . "1085-3375" . . "Article ID" .