## Triple solutions of constant sign for a system of Fredholm integral equations.(English)Zbl 1082.45004

Summary: We consider the following system of Fredholm integral equations $u_i(t)= \int^1_0g_i(t,s)P_i\bigl(s,u_1(s), u_2(s),\dots, u_n(s)\bigr) ds,\;t\in[0,1],\;1\leq i\leq n.$ Criteria for the existence of three constant-sign solutions of the system will be presented. The generality of the results obtained is illustrated through applications to several well known boundary value problems. We also consider a similar problem on the half-line $$[0,\infty)$$ $u_i(t)= \int^\infty_0g_i(t,s) P_i \bigl(s,u_1(s), u_2(s),\dots,u_(s)\bigr)ds,\quad t\in[0, \infty),\;1\leq i\leq n.$

### MSC:

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