Constant-sign solutions of a system of Fredholm integral equations (Q1431633)

The following system of Hammerstein integral equations is investigated \[ u_i(t)= \int^1_0 g_i(t,s) f_i(s, u_1(s), u_2(s),\dots, u_n(s))\,ds\tag{1} \] and \(i= 1,2,\dots, n\). A few theorems are proved on the existence of solutions (single, double or multiple) of the system (1) with constant sign. The obtained results are illustrated through applications to various types of boundary value problems. Moreover, the authors consider also the system of Hammerstein integral equations on half line of the form: \[ u_i(t)= \int^\infty_0 g_i(t,s) f_i(s, u_1(s), u_2(s),\dots, u_n(s))\,ds, \] \(t\in [0,\infty)\), \(i= 1,2,\dots, n\).