ON THE DETERMINATION OF ORBITS BY THE SOLUTION OF A SYSTEM OF INTEGRAL EQUATIONS

1966 ◽  
Author(s):  
V. T. Gontkovskaya
Keyword(s):  
Integral Equations ◽  
System Of Integral Equations

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.

Leading-Edge Corrections to the Linear Theory of Partially Cavitating Hydrofoils

1991 ◽  
Vol 35 (01) ◽  
pp. 15-27
Author(s):  
Spyros A. Kinnas
Keyword(s):  
Integral Equations ◽  
Linear Theory ◽  
Leading Edge ◽  
Foil Thickness ◽  
System Of Integral Equations ◽  
Cavitation Inception ◽  
Perturbation Velocity ◽  
Linearized Theory ◽  
Work First ◽  
Cavitating Hydrofoil

In this work, first, the partially cavitating hydrofoil problem is formulated in linear theory in terms of vorticity and source distributions on the projection of the hydrofoil to the free-stream direction. The resulting system of integral equations is inverted and the solution is expressed in terms of integrals of the horizontal perturbation velocity in fully wetted flow, multiplied by weighting functions that are independent of the shape of the hydrofoil. Second, the linearized dynamic boundary condition on the cavity is modified so that the total velocity on the cavity as predicted by applying Lighthill's leading-edge corrections is a constant. This results in a varying horizontal perturbation velocity on the cavity rather than a constant as required by conventional linear theory. The modified system of integral equations is inverted and the solution is expressed in terms of integrals of known quantities. The present linearized theory with the leading-edge corrections included, predicts a finite cavitation inception number as well as the correct effect of foil thickness on cavity size.

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