On blow-up solutions of nonautonomous quadratic differential systems

Stability analysis of Riccati differential equations related to affine diffusion processes

“…In this paper, we study the stability properties of the following class of quadratic differential systems: (1) where A is given as…”

Blow-up solutions of cubic differential systems

“…As an example of such application we consider the Cauchy-Dirichlet problem for systems of semilinear heat equations with cubic nonlinearities. We show how this problem can be reduced to problem (1). To the best of our knowledge, the obtained results have not been published yet in autonomous case.…”

“…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.…”

“…. , n. Here σ j , A j , b j , and c j are the same as in system (1). Note that in cubic forms σ j we replace x by u.…”

“…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).…”