Malkhaz Ashordia ON A TWO-POINT SINGULAR BOUNDARY VALUE PROBLEM FOR SYSTEMS OF NONLINEAR GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS

The two-point boundary value problem is considered for the system of nonlinear generalized ordinary differential equations with singularities on a non-closed interval. Singularity is understood in a sense of the vector-function corresponding to the system which belongs to the local Carathéodory class with respect to the matrix-function corresponding to the system. The general sufficient conditions are established for the unique solvability of this problem. Relying on these results, the effective conditions are established for the unique solvability of the problem. îâäæñéâ. ïæêàñèŽîëIJâIJæŽê àŽêäëàŽáëâIJñè øãâñèâIJîæã áæòâîâêùæŽèñî àŽêðëèâIJŽåŽ ïæïðâéæïŽåãæï àŽêýæèñèæŽ ëîûâðæèëãŽêæ ïŽïŽäôãîë ŽéëùŽêŽ ŽîŽøŽçâðæè æêðâîãŽèäâ. ïæêàñèŽîëIJŽ àŽæàâIJŽ æé Žäîæå, îëé ïæïðâéæï öâïŽIJŽéæïæ ãâóðëîñèæ òñêóùæŽ éæâçñåãêâIJŽ èëçŽèñî çŽîŽåâëáëîæï çèŽïï ïæïðâéæï öâïŽIJŽéæïæ éŽðîæùñèæ òñêóùææï éæéŽîå. éæôâIJñèæŽ Žé ŽéëùŽêæï ùŽèéýîæãŽá ŽéëýïêŽáëIJæï äëàŽáæ ïŽçéŽîæïæ ìæîëIJâIJæ. Žé öâáâàâIJäâ áŽõîáêëIJæå áŽáàâêæèæŽ ùŽèïŽýŽá ŽéëýïêŽáëIJæï âòâóðñîæ ïŽçéŽîæïæ ìæîëIJâIJæ. 2010 Mathematics Subject Classification. 34K06, 34K10.