On singular nonlinear distributional and impulsive initial and boundary value problems
Department of Mathematical Sciences, University of Oulu, BOX 3000, FIN-90014, Oulu, Finland
Boundary Value Problems 2011, 2011:24 doi:10.1186/1687-2770-2011-24Published: 16 September 2011
To derive existence and comparison results for extremal solutions of nonlinear singular distributional initial value problems and boundary value problems.
Fixed point results in ordered function spaces and recently introduced concepts of regulated and continuous primitive integrals of distributions. Maple programming is used to determine solutions of examples.
New existence results are derived for the smallest and greatest solutions of considered problems. Novel results are derived for the dependence of solutions on the data. The obtained results are applied to impulsive differential equations. Concrete examples are presented and solved to illustrate the obtained results.
MSC: 26A24, 26A39, 26A48, 34A12, 34A36, 37A37, 39B12, 39B22, 47B38, 47J25, 47H07, 47H10, 58D25