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On the Solution of the DE LA VALLÉE POUSSIN Problem by Using Quasilinearization

✍ Scribed by Ľudomír Šlahor

Publisher
John Wiley and Sons
Year
1979
Tongue
English
Weight
363 KB
Volume
87
Category
Article
ISSN
0025-584X

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✦ Synopsis

On the Solution of the DE LA VALLBE POUSSIN Problem by Using Quasilinearization LUDOM~R SLAHOR, Bratislava (Czechoslovakia) (Eingegangen am 7.7. 1976) 1. In solving the boundary-value problems from the theory of differential equations the method of quasilinearization has been used ([l], [a], [3], [4], 151 and [S]). In this paper by the method of quasiljnearization the boundary-value problem u@)=f(x, u, 4, . . . , U ( n -l ) ) u'""'(ak)=O ( j = l , 2 , . . . , nk; k = 1 , 2 , * . . , m ) ---=a =ai -= a 2 < . . . -=a, -=a, = b -= m u(i-')(al) =u(i-')(a+) (j= 1, 2, . . . , ni) ~u(i-l)(am)=u"-l)(b-) ( j = l , 2, . . . , n,) is solved where f ( x , u, 4, . . . , u(n-i)) is a non-linear function (scalar) of the arguments u, 4, . . . , u@-') which will be defined more accurately below and ai (i= = 1, 2, . . . , m ) are numbers. The theory of the DE LA VALL~E Poussw problem

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