ISSN 2079-6900 (Print) 
ISSN 2587-7496 (Online)

Middle Volga Mathematical Society Journal

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A pseudoparabolic type quasilinear integro-differential equation with degenerate kernel and integral condition

T. K. Yuldashev K. H. Shabadikov1

AnnotationNonlocal mixed-value problem for a quasinlinear pseudoparabolic type integro-differential equation with degenerate kernel and reflective first argument is considered. The questions of one-value solvability of such equations are examined. For equations of the third order the method of degenerate kernel is developed. Fourier method of variables’ separation is used. After some denoting the examined equation is reduced to a system of countable algebraic equations’ systems with complex right-hand side. After simple transformation countable system of nonlinear integral equations is obtained. One-value solvability of this system is proved by method of successive approximations combined with method of contractive mappings.
Keywordsnonlocal mixed-value problem, integro-differential equation, degenerate kernel, argument reflection, one-valued solvability

1Associate professor of Higher Mathematics Department, M. F. Reshetnev Siberian State Aerospace University, Krasnoyarsk, tursun.k.yuldashev@gmail.com

2Associate professor of Mathematical Analysis and Differential Equations Department, Fergana State University, Fergana, Uzbekistan, konak.shabadikov@mail.ru

Citation: T. K. Yuldashev K. H. Shabadikov, "[A pseudoparabolic type quasilinear integro-differential equation with degenerate kernel and integral condition]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:4 (2016) 76–88 (In Russian)