Multiple solutions for the system of Hammerstein nonlinear integral equations and an application (Q2731611)

The author investigates the existence of multiple nontrivial solutions of the following system of Hammerstein integral equations NEWLINE\[NEWLINE\begin{aligned} g(x) &= \int_G k_1(x,y) f_1(y,g(y),h(y)) dy,\\ h(x) &= \int_G k_2(x,y) f_2(y,g(y),h(y)) dy, \end{aligned} \tag{1}NEWLINE\]NEWLINE where \(G\) is a bounded closed subset of \(\mathbb{R}^n\), \(k_i\) is a nonnegative continuous function and \(f_i\) is a continuous function \((i=1,2)\). The main tool used in the considerations is the theory of topological degree. An application to a boundary value problem for a system of ordinary differential equations is also given.