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Constant-sign solutions of a system of Fredholm integral equations. (English) Zbl 1053.45004

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: \[ u_i(t)= \int^\infty_0 g_i(t,s) f_i(s, u_1(s), u_2(s),\dots, u_n(s))\,ds, \] \(t\in [0,\infty)\), \(i= 1,2,\dots, n\).

MSC:

45G15 Systems of nonlinear integral equations
45M20 Positive solutions of integral equations
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