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

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

Cubo 6, No. 3, 1-45 (2004).

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

Keywords:

system of Fredholm integral equations; existence; constant-sign solutions