Positive blow-up solutions of nonlinear models from real world dynamics
1 Department for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, Wien, A-1040, Austria
2 Department of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, Olomouc, 77146, Czech Republic
Boundary Value Problems 2014, 2014:121 doi:10.1186/1687-2770-2014-121
Dedicated to Professor Ivan Kiguradze for his merits in mathematical sciencesPublished: 16 May 2014
In this paper, we investigate the structure and properties of the set of positive blow-up solutions of the differential equation , , where . The differential equation is studied together with the boundary conditions , . We specify conditions for the data function h which guarantee that the set of all positive solutions to the above boundary value problem is nonempty. Further properties of the solutions are discussed and results of numerical simulations are presented.
MSC: 34B18, 34B16, 34A12.