Mathematics Commons^™

Solutions Of A System Of Integral Equations In Orlicz Spaces, Ravi P. Agarwal, Donal O'Regan, Patricia J.Y. Wong

Mathematics and System Engineering Faculty Publications

We consider the following system of integral equations Ui(t) = ∫1gi(t,s)fi(s,u1(s),u2(s),...,un(s))ds, a.e. t [0,1], 1 ≤ i ≤ n. Our aim is to establish criteria such that the above system has a solution (u±,U2,... ,un) where uiLφ (Orlicz space), 1 < i < n. We further investigate the system Ui(t) = ∫1gi(t,s)fi(s,u1(s),u2(s),...,un(s))ds, a.e. t [0,1], 1 ≤ i ≤ n. and establish the existence of constant-sign solutions in Orlicz spaces, i.e., for each 1 ≤ i ≤ n, Oui > 0 and ui G L