BLOW-UP BEHAVIOR OF HAMMERSTEINTYPE VOLTERRA INTEGRAL EQUATIONS

摘要

In this paper, we consider the blow-up behavior of Hammerstein-type Volterra integral equations. Based on several fundamental assumptions, some necessary and sufficient conditions under which the solution blows up in finite time are given. Some examples illustrate that there may always exist a global solution for a power-law function and that the blow-up behavior only depends upon the value of the kernel in a neighborhood of zero. As an application, we give some results on the blow-up behavior of Volterra integro-differential equations of Hammerstein-type.