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A STUDY ON A CLASS OF FOURTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS

Authors

Samed Aliyev, Arzu Aliyeva, Sardar Aliyev

Rubric:Materials Science
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Annotation

This work is dedicated to the study of certain properties of the almost everywhere solution to a one-dimensional mixed problem for one class of fourth order nonlinear equations. The almost everywhere solution of mixed problem under consideration is sought in the form of Fourier series. After applying Fourier method, the problem of finding unknown Fourier coefficients  of sought almost everywhere solution   is reduced to solving some countable system of nonlinear integral equations. 

Keywords

fourth order nonlinear equation
one-dimensional mixed problem
almost everywhere solution
Fourier method.

Authors

Samed Aliyev, Arzu Aliyeva, Sardar Aliyev

References:

S. Aliyev, M. Heydarova, A. Aliyeva. On the existence of classical solution to one-dimensional fourth order semilinear equations, Advances in Differential Equations and Control Processes 31 (2), 2024, 165-185.

S. Aliyev, A. Aliyeva, G. Abdullayeva. On the existence of solution to multidimensional third order nonlinear equations, European Journal of Pure and Applied Mathematics 12 (2), 2019, 577-589.

Azizbayov, E.I. The nonlocal inverse problem of the identification of the lowest coefficient and the right-hand side in a second-order parabolic equation with integral conditions. Bound Value Probl 2019, 11 (2019). https://doi.org/10.1186/s13661-019-1126-z

Azizbayov, E.I. Inverse coefficient identification problem for a hyperbolic equation with nonlocal integral condition. Turkish Journal of Mathematics 46(4): 2022, 1243-1255. https://doi.org/10.55730/1300-0098.3155

Davis P.L. On the existence of uniqueness and stability of solution of a nonlinear functional differential equation. J.Math. Anal. and Appl., 1971, 34(1), 128-140.

Khudaverdiyev K.I., Sadikhov M.N. On the existence in small for almost everywhere a solution of the one-dimensional mixed problem for a class of Korteweg-deVries-Burgers-type nonlinear equations. Bulletin of Baku State University, Series of Physical and Mathematical Sciences, 2008, No. 3 (Russian)

Khudaverdiyev K.I., Heydarova M.N. Investigation of almost everywhere a solution of the one-dimensional mixed problem for a fourth-order semilinear biparabolic equation. II. - Bulletin of Baku State University, Series of Physical and Mathematical Sciences, 2008, No. 2, pp. 5-15 (Russian).

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