On blow-up solutions of polynomial Kolmogorov systems

Blow-up solutions of cubic differential systems

“…The results of this paper may be considered as continuation and generalization of the results obtained in [1][2][3]. Our approach can be applied to systems of partial differential equations.…”

“…By the Cauchy-Schwartz inequality, we get x 2 (ω T x) 2 ω −2 . From this and (b 1 ) it follows that σ (t, x) a 3 (ω T x) 3 for ω T x M 0 . Let conditions (b 2 ) and (b 3 ) be satisfied.…”

“…Also in his monograph [12] D.H. Jacobson investigated these problems for autonomous quadratic differential systems. For nonautonomous differential systems problems (i) and (ii) are studied in [1][2][3]. In some other classes of differential equations and systems the blow-up phenomena have been studied by many authors (see, for example, [4][5][6][9][10][11][13][14][15][16][17] and references therein).…”

“…The proof of Theorem 9 is similar to that of Theorem 6. Using (d 1 ), we find σ (t, u) μ(ω T ω) −1 (ω T u) 3 . It also follows from (d 2 ) and (d 3 ) that…”