### Existence of positive solutions to systems of nonlinear integral or differential equations

DOI: http://dx.doi.org/10.12775/TMNA.2009.042

#### Abstract

In this paper, we are concerned with existence of positive

solutions for systems of nonlinear Hammerstein integral equations,

in which one nonlinear term is superlinear and the other is

sublinear. The discussion is based on the product formula of fixed

point index on product cone and fixed point index theory in cones.

As applications, we consider existence of positive solutions for

systems of second-order ordinary differential equations with

different boundary conditions.

solutions for systems of nonlinear Hammerstein integral equations,

in which one nonlinear term is superlinear and the other is

sublinear. The discussion is based on the product formula of fixed

point index on product cone and fixed point index theory in cones.

As applications, we consider existence of positive solutions for

systems of second-order ordinary differential equations with

different boundary conditions.

#### Keywords

Positive solution; Hammerstein integral equations; fixed point index; product cone

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