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    Solutions of a system of integral equations in orlicz spaces

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    Date
    2009-12-01
    Author
    Agarwal, Ravi P.
    O'Regan, Donal
    Wong, Patricia J.Y.
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    Cited 4 times in Scopus (view citations)
    
    Recommended Citation
    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
    Published Version
    http://doi.org/10.1216/jie-2009-21-4-469
    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 <= i <= 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 <= i <= 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 <= i <= nand establish the existence of constant-sign solutions in Orlicz spaces, i.e., for each 1 <= i <= n, theta u(i) >= 0 and u(i) is an element of L(phi), where theta is an element of {1, -1} is fixed.
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    http://hdl.handle.net/10379/10162
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