Positive solutions for a system of nonlinear singular Hammerstein integral equations via nonnegative matrices and applications
Using the fixed point index on a cone, the existence of a (strictly) positive solution of a system of Hammerstein integral equations with nonnegative kernels and nonnegative nonlinearities is obtained. The main hypothesis is that the nonlinearity has near zero (resp.\ globally) a growth which (with respect to the order) is comparable with the growth of a certain positive matrix. The result is applied to obtain a positive radial solution of a nonlinear elliptic equation on an annulus.
system of nonlinear singular Hammerstein integral equations
scientific article; zbMATH DE number 6121308