Existence of Eigenvalues of a Class of Integral Equations Arising in Laser Theory

Abstract

It is proved that the integral equation $int_{-1}^{1}G(x)F(xy)H(y)f(y)dy = lambda f(x)$ has at least one nonzero eigenvalue if F is any integral function of finite order, G and H are any bounded functions on [ 1,1], and the trace o...