On One Method of Solving Singularly Perturbed Systems of Tikhonov’s Type

On a nonlinear differential equation in a Banach space

“… ëþáîì ñëó÷àå, âñòàåò âîïðîñ î õàðàêòåðå ñõîäèìîñòè ïîñòðîåííîãî ðÿäà.  ðåãóëÿðíîé òåîðèè âîçìóùåíèé (îñîáåííî ëèíåéíîé) âî ìíîãèõ ñëó÷àÿõ íàáëþäàåòñÿ ãîëîìîðôíàÿ çàâèñèìîñòü ðåøåíèÿ îò ïàðàìåòðà [3], â ñèíãóëÿðíîì ñëó÷àå ñõîäèìîñòü, êàê ïðàâèëî, àñèìïòîòè÷åñêàÿ [2,5,6], õîòÿ è èìåþòñÿ óñëîâèÿ îáû÷íîé ñõîäèìîñòè [7,8]. Îäíàêî, åñëè çàäà÷à íåëèíåéíàÿ, òî ïðîáëåìà îáû÷íîé ñõîäèìîñòè òðåáóåò ãëóáîêîãî èññëåäîâàíèÿ (îñîáåííî, åñëè âîçìóùàþùèé îïåðàòîð íåëèíåéíûé).…”

Analytical Aspects of the Theory of Tikhonov Systems

“…Consider the boundary value problem for the Tikhonov system in the case where k = m = 2 (the case of one fast variable is studied in [8]). As a result, we have a system…”

“…In [8], the conditions for the existence of pseudoholomorphic solutions of initial problems for Tikhonov systems with one slow variable were given. In this paper, the number of fast and slow variables can be arbitrary.…”