Existence of solutions of systems of Volterra integral equations via Brezis-Browder arguments

Abstract

We consider two systems of Volterra integral equations $$ u_i(t)=h_i(t) + int_{0}^{t}g_i(t,s)f_i(s,u_1(s),u_2(s),dots, u_n(s))ds, quad 1leq ileq n $$ where t is in the closed interval $[0,T]$, or in the half-open interval $[0,T)$. By an argument originated from Brezis and Browder [8], criteria are offered for the existence of solutions of the systems of Volterra integral equations. We further establish the existence of constant-sign solutions, which include positive solutions (the usual consideration) as a special case. Some examples are also presented to illustrate the results obtained.

Keywords

• System of Volterra integral equations
• Brezis-Browder argument