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In this article, the contraction mapping principle and Liapunov's method are used to study qualitative properties of nonlinear Volterra equations of the form $x(t) = a(t) -\int^{t}_{0}C(t,s)g(s,x(s))\;ds,t\geq0.$ In particular, the existence of bounded solutions and solutions with various $L^p$ properties are studied under suitable conditions on the functions involved with this equation.