On the asymptotic behavior of solutions of integral equations

1979 ◽  
pp. 137-148 ◽  
Author(s):  
J. J. Levin
Keyword(s):  
Asymptotic Behavior ◽  
Integral Equations ◽  
Asymptotic Behavior Of Solutions

scholarly journals Asymptotic Behavior of Solutions of Integral Equations with Homogeneous Kernels

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 180
Author(s):  
Oleg Avsyankin
Keyword(s):  
Integral Equation ◽  
Asymptotic Behavior ◽  
Integral Equations ◽  
Spherical Harmonics ◽  
Special Class ◽  
Continuous Functions ◽  
Asymptotic Behavior Of Solutions ◽  
Free Term ◽  
Research Technique ◽  
Multidimensional Integral

The multidimensional integral equation of second kind with a homogeneous of degree (−n) kernel is considered. The special class of continuous functions with a given asymptotic behavior in the neighborhood of zero is defined. It is proved that, if the free term of the integral equation belongs to this class and the equation itself is solvable, then its solution also belongs to this class. To solve this problem, a special research technique is used. The above-mentioned technique is based on the decomposition of both the solution and the free term in spherical harmonics.

scholarly journals Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-18 ◽  
Author(s):  
E. Messina ◽  
Y. Muroya ◽  
E. Russo ◽  
A. Vecchio
Keyword(s):  
Asymptotic Behavior ◽  
Numerical Methods ◽  
Integral Equations ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Volterra Integral Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Nonlinear Difference Equations ◽  
Discrete Equations

We consider nonlinear difference equations of unbounded order of the formxi=bi−∑j=0iai,jfi−j(xj),  i=0,1,2,…,wherefj(x)  (j=0,…,i)are suitable functions. We establish sufficient conditions for the boundedness and the convergence ofxiasi→+∞. Some of these conditions are interesting mainly for studying stability of numerical methods for Volterra integral equations.

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