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

Agarwal, Ravi P.; O’Regan, Donal; Wong, Patricia J. Y.

Acta Appl. Math. 80, No. 1, 57-94 (2004).

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

Reviewer: J. Banaś (Rzeszów)

MSC:

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

Keywords:

constant-sign solutions; system of Fredholm integral equations; system of Hammerstein integral equations; boundary value problems