Oscillatory Solution of a Convolutional Volterra Integral Equation
Henry Otoo *
University of Mines and Technology, Tarkwa, Ghana.
William Obeng-Denteh
Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
Lewis Brew
University of Mines and Technology, Tarkwa, Ghana.
*Author to whom correspondence should be addressed.
Abstract
Oscillatory solutions play a pivotal role in understanding functional differential and integral equations, offering insights into the behaviour of these equations' solutions, and assisting in understanding their growth, stability, and convergence properties. This study establishes the oscillatory solution of a convolutional Volterra integral equation using mathematical proofs. Theorems for oscillatory solutions are proposed and proven based on well-defined assumptions, along with an illustrated example. The proofs presented herein reveal that the convolutional Volterra integral equation can exhibit oscillatory or non-oscillatory behavior, contingent upon the characteristics of the function within the integral.
Keywords: Convolution, volterra integral equation, oscillatory, infimum, supremum