System of Integral Equations for Solving an Inverse Problem for a Quasilinear Hyperbolic Equation

2019 ◽  
Vol 55 (9) ◽  
pp. 1143-1149 ◽  
Author(s):  
A. M. Denisov
Keyword(s):  
Inverse Problem ◽  
Hyperbolic Equation ◽  
Integral Equations ◽  
System Of Integral Equations ◽  
Quasilinear Hyperbolic Equation

scholarly journals On the definition of a time-dependent lower coefficient in a third-order hyperbolic equation

2021 ◽  
pp. 9-18
Author(s):  
Б.С. Аблабеков ◽  
А.К. Жороев
Keyword(s):  
Inverse Problem ◽  
Hyperbolic Equation ◽  
Unknown Coefficient ◽  
Existence And Uniqueness Theorem ◽  
Third Order ◽  
Volterra Type ◽  
System Of Integral Equations ◽  
Additional Information ◽  
Order Hyperbolic Equation ◽  
Definition Of

В работе рассматривается обратная задача для гиперболического уравнения третьего порядка. Ставится обратная задача, состоящая в определении неизвестного коэффициента, зависящего от времени. В качестве дополнительной информации для решения обратной задачи задаются значения решения задачи во внутренней точке. Доказывается теорема существования и единственности решения обратной задачи. Доказательство основано на выводе нелинейной системы интегральных уравнений типа Вольтерра второго рода и доказательстве его разрешимости. The paper deals with an inverse problem for a hyperbolic equation of the third order. An inverse problem is posed, which consists in determining an unknown coefficient that depends on time. As additional information for solving the inverse problem, we set the values of the solution to the problem at an interior point, and prove the existence and uniqueness theorem for the solution of the inverse problem. The proof is based on the derivation of a nonlinear system of integral equations of the Volterra type of the second kind and the proof of its solvability.

scholarly journals Solvability of an infinite system of integral equations on the real half-axis

2020 ◽  
Vol 10 (1) ◽  
pp. 202-216
Author(s):  
Józef Banaś ◽  
Weronika Woś
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Main Tool ◽  
Supremum Norm ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness ◽  
System Of Integral Equations ◽  
The Real ◽  
Half Axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

Constant-Sign Lp Solutions for a System of Integral Equations

2004 ◽  
Vol 46 (3-4) ◽  
pp. 195-219 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O’Regan ◽  
Patricia J. Y. Wong
Keyword(s):  
Integral Equations ◽  
Constant Sign ◽  
System Of Integral Equations ◽  
Lp Solutions

scholarly journals Fixed Point Results for the Family of Multivalued F-Contractive Mappings on Closed Ball in Complete Dislocated b-Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 56 ◽  
Author(s):  
Qasim Mahmood ◽  
Abdullah Shoaib ◽  
Tahair Rasham ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Closed Ball ◽  
Multivalued Mappings ◽  
System Of Integral Equations ◽  
Contractive Mappings ◽  
The Family ◽  
Rational Type

The purpose of this paper is to find out fixed point results for the family of multivalued mappings fulfilling a generalized rational type F-contractive conditions on a closed ball in complete dislocated b-metric space. An application to the system of integral equations is presented to show the novelty of our results. Our results extend several comparable results in the existing literature.

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