A CLASS OF ABSTRACT VOLTERRA EQUATIONS, VIA WEAKLY PICARD OPERATORS TECHNIQUE

作者：Serban M A^*; Rus I A; Petrusel A

来源：Mathematical Inequalities & Applications, 2010, 13(2): 255-269.

DOI：10.7153/mia-13-21

• L-space
• gauge space
• weakly Picard operator
• abstract Volterra equation
• Volterra integral equation
• functional-integral equation
• solution set
• data dependence
• comparison theorem
• operatorial inequalities

In this paper we consider the following abstract Volterra equations:
x(t) = G(t, g(x)(t), x(t), x(0)) + integral(t)(-t) K(t, s, x(s), x(h(s))), t is an element of R
and
x(t) = G(t, g(x)(t), x(t), x (0)) + integral(vertical bar t vertical bar)(-vertical bar t vertical bar) K(t, s, x (s), x(h(s))) ds, t is an element of R.
Using the weakly Picard operator technique we establish existence, data dependence and comparison results for the solution. The derivability of the solutions with respect to a parameter is also studied.

• 出版日期2010-4