Boundary Value Problems
Volume 2008 (2008), Article ID 236386, 9 pages
Nonlinear Systems of Second-Order ODEs
Departamento de Matemática y C. C., Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile
Received 2 February 2007; Accepted 16 November 2007
Academic Editor: Jean Mawhin
Copyright © 2008 Patricio Cerda and Pedro Ubilla. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study existence of positive solutions of the nonlinear system in ; in ; , where and . Here, it is assumed that , are nonnegative continuous functions, , are positive continuous functions, , , and that the nonlinearities satisfy superlinear hypotheses at zero and
. The existence
of solutions will be obtained using a combination among the method of truncation, a
priori bounded and Krasnosel'skii well-known result on fixed point indices in cones. The
main contribution here is that we provide a treatment to the above system considering
differential operators with nonlinear coefficients. Observe that these coefficients may
not necessarily be bounded from below by a positive bound which is independent of and .