Qualitative properties of nonlinear Volterra integral equations

M. Islam, University of Dayton, Dayton, U.S.A.
J. T. Neugebauer, University of Dayton, Dayton, U.S.A.

E. J. Qualitative Theory of Diff. Equ., No. 12. (2008), pp. 1-16.

Abstract: 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.

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