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Constant-Sign Solutions Of A System Of Integral Equations With Integrable Singularities, Ravi P. Agarwal, Donal O'Regan, Patricia J.Y. Wong

Mathematics and System Engineering Faculty Publications

We consider the following systems of Fredholm integral equations and the system of Volterra integral equations where the nonlinearities fi, 1 ≤ i ≤ n may be singular in the independent variable and may also be singular at uj = 0, j ∈ {1, 2,..., n}. Our aim is to establish criteria such that the above systems have at least one constant-sign solution (u1, u2,..., un), i.e., for each 1 ≤ i ≤ n, Θiui ≥ 0 where Θi ∈ {1,-1} is fixed. © 2007 Rocky Mountain Mathematics Consortium.