A Volterra Equation with Square Integrable Solution

Olof J. Staffans
1980 Proceedings of the American Mathematical Society  
We study the asymptotic behavior of the solutions of the nonlinear Volterra integrodifferential equation x'(t) + fa(t-s)g(x(s)) ds =/(/) (t e R +). •'o Here R + = [0, oo), a, g and / are given real functions, and x is the unknown solution. In particular, we give sufficient conditions which imply that x and x' are square integrable.
doi:10.2307/2042255 fatcat:wiinogzyvnc23ln5hh3qceeihi