## Solutions of a system of integral equations in orlicz spaces

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2009-12-01##### Author

Agarwal, Ravi P.

O'Regan, Donal

Wong, Patricia J.Y.

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Agarwal, Ravi P. O'Regan, Donal; Wong, Patricia J.Y. (2009). Solutions of a system of integral equations in orlicz spaces. Journal of Integral Equations and Applications 21 (4), 469-498

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##### Abstract

We consider the following system of integral equations
u(i)(t) = integral(1)(0) g(i)(t, s)f(i) (s, u(1)(s), u(2)(s),...,u(n)(s)) ds,
a.e. t is an element of [0,1]. 1 &lt;= i &lt;= n.
Our aim is to establish criteria such that the above system has a solution (u(1), u(2),..., u(n)) where u(i) is an element of L(phi) (Orlicz space), 1 &lt;= i &lt;= n. We further investigate the system
u(i)(t) = integral(1)(0) g(i)(t, s)H(s, u(1)(s), u(2)(s),...,u(n)(s))ds,
a.e. t is an element of[0, 1], 1 &lt;= i &lt;= nand establish the existence of constant-sign solutions in Orlicz spaces, i.e., for each 1 &lt;= i &lt;= n, theta u(i) &gt;= 0 and u(i) is an element of L(phi), where theta is an element of {1, -1} is fixed.