On two pairs of simultaneous dual integral equations

Summary This paper considers a system of coupled pairs of dual integral equations with constant coefficients involving Bessel functions of orders zero and unity. A solution is obtained in terms of the coefficients by reducing the system to a single integral equation of the Wiener-Hopf type with both the sum and difference kernels present.A simple transformation of the system causes the coefficient of the sum kernel to vanish. The transformation leaves the Wiener-Hopf equation unaltered except for the coefficients which become complex. An equation of this type was solved by Spence in 1967. Although Spence's solution does not cover complex coefficients it can be modified to do so.The result is quoted in this paper and is used to solve the system of coupled pairs of dual integral equations of the present paper.The adhesive contact problem recently solved by Gladwell is one in which the solution technique of the present paper has proved useful.On leave of absence from the Department of Mathematics, University of Southampton.