Nonlinear Systems of Second-Order ODEs
Departamento de Matemática y C. C., Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile
Boundary Value Problems 2008, 2008:236386 doi:10.1155/2008/236386Published: 10 December 2007
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 .