scholarly journals On the second type linear volterra integral equations with convolution kernel

1992 ◽  
pp. 027-033
Author(s):  
Mustafa BALCI ◽  
Ö. Faruk TEMİZER
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Convolution Kernel ◽  
Linear Volterra Integral Equations

scholarly journals Periodic solutions of Volterra integral equations

1988 ◽  
Vol 11 (4) ◽  
pp. 781-792 ◽  
Author(s):  
M. N. Islam
Keyword(s):  
Periodic Solutions ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Volterra Integral Equations ◽  
System Of Equations ◽  
Convolution Kernel ◽  
Basic Tool ◽  
Resolvent Function

Consider the system of equationsx(t)=f(t)+∫−∞tk(t,s)x(s)ds,           (1)andx(t)=f(t)+∫−∞tk(t,s)g(s,x(s))ds.       (2)Existence of continuous periodic solutions of (1) is shown using the resolvent function of the kernelk. Some important properties of the resolvent function including its uniqueness are obtained in the process. In obtaining periodic solutions of (1) it is necessary that the resolvent ofkis integrable in some sense. For a scalar convolution kernelksome explicit conditions are derived to determine whether or not the resolvent ofkis integrable. Finally, the existence and uniqueness of continuous periodic solutions of (1) and (2) are btained using the contraction mapping principle as the basic tool.

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