Nonlocal boundary value problem for a differential-operator equation with nonlinear right part in a complex domain (in Ukrainian) |
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| Author |
ilkivv@i.ua, n.strap@i.ua
National University Lviv Polytechnic
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| Abstract |
The paper is devoted to investigation of nonlocal boundary value problem for a differential-operator equation
with the nonlinear right part and with the operator $B=(B_1,\dotsc,B_p)$, where
$B_j\equiv z_j\frac{\partial}{\partial z_j}$, $j=1,\dotsc,p$, --- 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.
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| Keywords |
differential equation; generalized differentiation; small denominators; the Nash-Moser scheme
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| DOI |
doi:10.15330/ms.45.2.170-181
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| Reference |
1. Ptashnyk B.Yo., Il’kiv V.S., Kmit’ I.Ya., Polishchuk V.M. Nonlocal boundary value problems for partial
differential equations, Kiev: Naukova Dumka, 2002. – 415 š. (in Ukrainian)
2. Eloea Paul W., Ahmadb Bashir, Positive solutions of a nonlinear n-th order boundary value problem with nonlocal conditions, J. Applied Mathematics Letters, 18 (2005), ¹5, 521–527. 3. Borok V.M., Fardigola L.V. Nonlocal well-posed boundary-value problems in a layer. Mathematical notes, 48 (1990), ¹1, 20–25. (in Russian) 4. Kalenyuk P.I., Nytrebych Z.M., Kohut I.V. Problem with nonlocal two-point condition in time variable for homogeneous partial differential equation of infinite order in spatial variables. Math.Methods Phys. Mech. Fields, 51 (2008), ¹4, 17–26. (in Ukrainian) 5. Berti M., Bolle P., Cantor families of periodic solutions of wave equations with $C^k$ nonlinearities, Nonlinear Differential Equations and Applications, 15 (2008), 247–276. 6. Berti M., Bolle P., Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions, Arch. Rational Mech. Anal. 195, (2010), ¹2, 609–642. 7. Berti M., Bolle P., Cantor families of periodic solutions for completely resonant nonlinear wave equations, Duke Math. J. 134, (2006), ¹2, 359–419. |
| Pages |
170-181
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| Volume |
45
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| Issue |
2
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| Year |
2016
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |