On the Maximal Interval of Existence for Solutions to Some Non-Linear Volterra Integral Equations with Convolution Kernel

1996 ◽  
Vol 28 (1) ◽  
pp. 59-65 ◽  
Author(s):  
P. J. Bushell ◽  
W. Okrasinski
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Convolution Kernel ◽  
Maximal Interval ◽  
Non Linear ◽  
Linear Volterra Integral Equations

On a class of Volterra and Fredholm non-linear integral equations

1976 ◽  
Vol 79 (2) ◽  
pp. 329-335 ◽  
Author(s):  
P. J. Bushell
Keyword(s):  
Integral Equations ◽  
Kernel Function ◽  
Existence And Uniqueness ◽  
Volterra Integral Equations ◽  
Fredholm Equations ◽  
Non Linear ◽  
Linear Volterra Integral Equations ◽  
Linear Integral ◽  
Image Position ◽  
Linear Integral Equations

This paper concerns the existence and uniqueness of non-negative solutions of non-linear Volterra integral equations of the typeandwhere the kernel function k(.,.) is non-negative and sufficiently smooth, and either 0 < p < 1 or – 1 < p < 1. We will consider also the corresponding Fredholm equationsand

Uniqueness of solutions for a class of non-linear Volterra integral equations with convolution kernel

1989 ◽  
Vol 106 (3) ◽  
pp. 547-552 ◽  
Author(s):  
P. J. Bushell ◽  
W. Okrasinski
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Convolution Kernel ◽  
Qualitative Behaviour ◽  
Uniqueness Of Solutions ◽  
Linear Diffusion ◽  
Non Linear ◽  
Linear Volterra Integral Equations ◽  
Image Position

The non-linear Volterra integral equationhas been studied recently in connection with non-linear diffusion and percolation problems [4, 6, 10]. The existence, uniqueness and qualitative behaviour of non-negative, non-trivial solutions are the questions of physical interest.

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