2015
DOI: 10.15330/ms.45.2.170-181
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Nonlocal boundary value problem for a differential-operator equation with nonlinear right part in a complex domain (in Ukrainian)

Abstract: . . , p, -operators of the generalized differentiation on complex variable z j . This problem is incorrect in the Hadamard sense and its sobvability related to the small denominators. By using of the Nash-Mozer iteration scheme the conditions of the sobvability of the problem in the scale of spaces of functions of several complex variables are established.1. Вступ. Дослiдження нелокальних крайових задач для рiзних типiв диференцiаль-них рiвнянь i систем рiвнянь з частинними похiдними та встановлення умов корек… Show more

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Cited by 3 publications
(2 citation statements)
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“…The operator method of studying the two-point problem in the strip in the Sobolev spaces is described in [12]. The two-point nonlocal problems for the weakly nonlinear differential-operator equations in the complex domain in the scales and specified scales of Sobolev spaces as well as in the scales of Dirichlet-Taylor spaces are studied by the Nash-Moser method in [29], [31] and [30], respectively. The solvability of the multipoint problems for the systems of quasilinear hyperbolic equations is proved by applying some fixed point theorems in [4,5,7,10,49].…”
mentioning
confidence: 99%
“…The operator method of studying the two-point problem in the strip in the Sobolev spaces is described in [12]. The two-point nonlocal problems for the weakly nonlinear differential-operator equations in the complex domain in the scales and specified scales of Sobolev spaces as well as in the scales of Dirichlet-Taylor spaces are studied by the Nash-Moser method in [29], [31] and [30], respectively. The solvability of the multipoint problems for the systems of quasilinear hyperbolic equations is proved by applying some fixed point theorems in [4,5,7,10,49].…”
mentioning
confidence: 99%
“…. , p, were considered in the papers [7][8][9][10]. By using of the Nash-Mozer iteration scheme, conditions of the solvability of the problems in the Sobolev spaces were established for the functions of several complex variables, in the Hörmander-Hilbert spaces and in the scale of spaces of functions, which are Dirichlet-Taylor series with fixed spectrum.…”
mentioning
confidence: 99%