The Research of Solving Inverse Problems of Complex Differential Equations

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

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Loaded differential equations and linear inverse problems for elliptic equations

Complex Variables and Elliptic Equations ◽

10.1080/17476933.2020.1793970 ◽

2020 ◽

pp. 1-19

Author(s):

A.I. Kozhanov ◽

T. N. Shipina

Keyword(s):

Inverse Problems ◽

Differential Equations ◽

Elliptic Equations ◽

Linear Inverse Problems

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On the Exact Solutions of Two (3+1)-Dimensional Nonlinear Differential Equations

Journal of Function Spaces ◽

10.1155/2020/5740310 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Fanning Meng ◽

Yongyi Gu

Keyword(s):

Differential Equations ◽

Exact Solutions ◽

Shallow Water ◽

Traveling Wave ◽

Nonlinear Differential Equations ◽

Complex Method ◽

Meromorphic Solutions ◽

Complex Differential Equations ◽

Bkp Equation

In this article, exact solutions of two (3+1)-dimensional nonlinear differential equations are derived by using the complex method. We change the (3+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation and generalized shallow water (gSW) equation into the complex differential equations by applying traveling wave transform and show that meromorphic solutions of these complex differential equations belong to class W, and then, we get exact solutions of these two (3+1)-dimensional equations.

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Growth of Meromorphic Function Sharing Functions and Some Uniqueness Problems

Journal of Function Spaces ◽

10.1155/2016/6250867 ◽

2016 ◽

Vol 2016 ◽

pp. 1-9

Author(s):

Jianming Qi ◽

Fanning Meng ◽

Wenjun Yuan

Keyword(s):

Meromorphic Function ◽

Differential Equations ◽

Meromorphic Functions ◽

Meromorphic Solutions ◽

Complex Differential Equations ◽

Function Sharing

Estimating the growth of meromorphic solutions has been an important topic of research in complex differential equations. In this paper, we devoted to considering uniqueness problems by estimating the growth of meromorphic functions. Further, some examples are given to show that the conclusions are meaningful.

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