Positive solutions of nonlinear Dirichlet BVPs in ODEs with time and space singularities
1 Department of Mathematical Analysis, Faculty of Science, Palacký University, 17. listopadu 12, Olomouc, CZ-771 46, Czech Republic
2 Department of Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, Wien, A-1040, Austria
Boundary Value Problems 2013, 2013:6 doi:10.1186/1687-2770-2013-6Published: 16 January 2013
In this paper, we discuss the existence of positive solutions to the singular Dirichlet boundary value problems (BVPs) for ordinary differential equations (ODEs) of the form
where . The nonlinearity may be singular for the space variables and/or . Moreover, since , the differential operator on the left-hand side of the differential equation is singular at . Sufficient conditions for the existence of positive solutions of the above BVPs are formulated and asymptotic properties of solutions are specified. The theory is illustrated by numerical experiments computed using the open domain MATLAB code bvpsuite, based on polynomial collocation.
MSC: 34B18, 34B16, 34A12.