Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 104, pp. 1-19.
Title: Existence of solutions of systems of Volterra integral equations
via Brezis-Browder arguments
Authors: Ravi P. Agarwal (Texas A&M Univ., Kingsville, TX, USA)
Donal O'Regan (National Univ. of Ireland, Galway, Ireland)
Patricia J. Y. Wong (Nanyang Technological Univ., Singapore)
Abstract:
We consider two systems of Volterra integral equations
$$
u_i(t)=h_i(t) + \int_{0}^{t}g_i(t,s)f_i(s,u_1(s),u_2(s),\dots,
u_n(s))ds, \quad 1\leq i\leq n
$$
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.
Submitted April 26, 2011. Published August 16, 2011.
Math Subject Classifications: 45B05, 45G15, 45M20
Key Words: System of Volterra integral equations; Brezis-Browder argument.