System of nonlinear integral equations

jannyhuggy · Dec 11, 2012

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!

jannyhuggy · Dec 12, 2012

I tried two iteration methods but perturbations seem to be divergent. Perhaps any regularization ideas?

System of nonlinear integral equations

Discussion

Undergrad Why ##a^0=1##?

Undergrad Finding the minimum distance between two curves

Undergrad Mixed approximation vs. full approximation for a power series expansion

Undergrad Best way to numerically solve this system of equations?

Undergrad Correct Upper/Lower limits for continuation of solutions for ODE

Undergrad Correct Upper/Lower limits for continuation of solutions for ODE

Graduate About ellipticity and a proof that a system of PDEs is elliptic

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

System of nonlinear integral equations

Discussion

Similar threads

Graduate System of nonlinear differential equations

Undergrad Is fx = ∫ exp(√(1-x²)) dx a nonlinear integral equation?

Undergrad Solving a System of Nonlinear Equations Symbolically

Graduate How can I solve a system of nonlinear differential equations with constants?

Graduate Using Mathematica to solve 2nd order system of nonlinear ODE's

Undergrad Test for inconsistency of system of nonlinear equations

Solving a system of nonlinear equations

Graduate F.E.M and Hamilton's Principle (converting differential equations into integral equations)

Graduate System of ODEs with bilinear terms: x'=a1*x*z, y'=b1*x + b2*y, z'=c1 + c2*z + c3*y*z

Graduate Is there a general method for solving Fredholm integral equations?

Graduate System of ODEs with bilinear terms: x'=a1xz, y'=b1x + b2y, z'=c1 + c2z + c3y*z