A nonuniqueness criterion for a singular system of two ordinary differential equations

Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations

“…There are numerous papers and books dealing with singular initial value problems (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and the references therein). Among others, we should mention pioneering results on the solvability of singular problems for ordinary differential equations achieved by Chechyk [15] and Kiguradze [13].…”

Singular Initial Value Problem for a System of Integro‐Differential Equations

“…Singular initial value problem for ordinary differential and integro-differential equations is fairly well studied see, e.g., 1-16 , but the asymptotic properties of the solutions of such equations are only partially understood. Although the singular initial value problems were widely considered using various methods see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13]16 , our approach to this problem is essentially different from others known in the literature. In particular, we use a combination of the topological method of T. Ważewski 8 and Schauder's fixed point theorem 11 .…”

Singular Cauchy Initial Value Problem for Certain Classes of Integro-Differential Equations

“…The singular Cauchy problem for first-order differential and integro-differential equations resolved or unresolved with respect to the derivatives of unknowns is fairly well studied see, e.g., 1-16 , but the asymptotic properties of the solutions of such equations are only partially understood. Although the singular Cauchy problems were widely considered by using various methods see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][16][17][18] , the method used here is based on a different approach. In particular, we use a combination of the topological method of T. Ważewski see, e.g., 19, 20 and Schauder's fixed point theorem 21 .…”