Computation of fixed point index and its applications

Abstract

In this paper, we make the nonlinear double integral equation of Hammerstein type the background of the research. Computation for the fixed point index of operators such as $A=K_{1}F_{1}K_ {2}F_{2}$ is given. As applications of the main results, we investigate the existence of positive solutions to the nonlinear double integral equation of Hammerstein type and the boundary value problem for the system of elliptic partial differential equations.