System of singular second-order differential equations with integral condition on the positive half-line

In this work, we are concerned with the existence and the multiplicity of nontrivial positive solutions for a boundary value problem of a system of second-order differential equations subject to an integral boundary condition and posed on the positive half-line. The positive nonlinearities depend on the solution and their derivatives and may have space singularities. New existence results of single and multiple solutions are obtained by means of the fixed point index theory on special cones in some weighted Banach space. Examples with numerical computations are included to illustrate the obtained existence theorems. This paper surveys and generalizes previous works.