System of nonlinear integral equations

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SUMMARY

The discussion centers on solving a system of nonlinear integral equations, with specific inquiries about the existence of solutions, approximate methods for solution production, and exact solution techniques. The user has attempted two iterative methods but encountered divergence issues, prompting a request for regularization strategies. Key points include the need for understanding the conditions under which solutions exist and exploring alternative methods for handling perturbations in the equations.

PREREQUISITES
  • Understanding of nonlinear integral equations
  • Familiarity with iterative methods for solving equations
  • Knowledge of regularization techniques in numerical analysis
  • Basic concepts of perturbation theory
NEXT STEPS
  • Research methods for proving the existence of solutions to nonlinear integral equations
  • Explore regularization techniques applicable to divergent iterative methods
  • Learn about alternative numerical methods for solving integral equations, such as the Galerkin method
  • Investigate specific perturbation methods and their applications in nonlinear analysis
USEFUL FOR

Mathematicians, physicists, and engineers dealing with nonlinear integral equations, as well as researchers looking for numerical solutions and regularization techniques.

jannyhuggy
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Hello everybody!

While solving some physical problem I got stuck with some system of integral equations.
The problem is formulated in .pdf file below.

I will be over-satisfied with the following
1) to know whether and why this system has/doesn't have a solution
2) how it could be produced approximately
3) if there are any methods for exact solution of equations of such a type, perhaps with other V(k)

View attachment 11111.pdf

ANY comments are highly welcome!
 
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I tried two iteration methods but perturbations seem to be divergent. Perhaps any regularization ideas?
 

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