Open Access Research

On singular nonlinear distributional and impulsive initial and boundary value problems

Seppo Heikkilä

Author Affiliations

Department of Mathematical Sciences, University of Oulu, BOX 3000, FIN-90014, Oulu, Finland

Boundary Value Problems 2011, 2011:24  doi:10.1186/1687-2770-2011-24

Published: 16 September 2011

Abstract

Purpose

To derive existence and comparison results for extremal solutions of nonlinear singular distributional initial value problems and boundary value problems.

Main methods

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.

Results

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

Keywords:
distribution; primitive; integral; regulated; continuous; initial value problem; boundary value problem; singular; distributional