Abstract
This paper, together with a recent paper by the second author on convex singular kernels, establishes a base for further investigation of mildly singular equations with Liapunov theory. We study the two nonlinear scalar integral equations x(t)=a(t)−∫0tD(t,s)[x(s)+G(s,x(s))]ds and z(t)=a(t)−∫0tD(t,s)g(s,z(s))ds where D has a singularity at t=s. The first equation is decomposed into three other simpler equations. We then construct a Liapunov functional for each of the equations which will yield Lp properties of the solutions.
Published Version
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