On singular nonlinear distributional and impulsive initial and boundary value problems

• Main Author: Heikkilä Seppo
• Format: Article
• Language: English
• Published: SpringerOpen 2011-01-01
• Series: Boundary Value Problems
• Subjects: distribution; primitive; integral; regulated; continuous; initial value problem; boundary value problem; singular; distributional
• Online Access: http://www.boundaryvalueproblems.com/content/2011/1/24
• ISSN: 1687-2762; 1687-2770

<p>Abstract</p> <p>Purpose</p> <p>To derive existence and comparison results for extremal solutions of nonlinear singular distributional initial value problems and boundary value problems.</p> <p>Main methods</p> <p>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.</p> <p>Results</p> <p>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.</p> <p><b>MSC: </b>26A24, 26A39, 26A48, 34A12, 34A36, 37A37, 39B12, 39B22, 47B38, 47J25, 47H07, 47H10, 58D25</p>