Singular Differential and Integral Equations with Applications

by Ravi P. Agarwal

Preface. 1: Differential Equations Singular in the Independent Variable. 1.1. Introduction. 1.2. Preliminaries. 1.3. Initial Value Problems. 1.4. Boundary Value Problems. 1.5. Bernstein Nagumo Theory. 1.6. Method of Upper and Lower Solutions. 1.7. Solutions in Weighted Spaces. 1.8. Existence Results Without Growth Restrictions. 1.9. Nonresonant Problems. 1.10. Nonresonant Problems of Limit Circle Type. 1.11. Nonresonant Problems of Dirichlet Type. 1.12. Resonance Problems. 1.13. Infinite Interval Problems I. 1.14. Infinite Interval Problems II. 2: Differential Equations Singular in the Dependent Variable. 2.1. Introduction. 2.2. First Order Initial Value Problems. 2.3. Second Order Initial Value Problems. 2.4. Positone Problems. 2.5. Semipositone Problems. 2.6. Singular Problems. 2.7. An Alternate Theory for Singular Problems. 2.8. Singular Semipositone Type Problems. 2.9. Multiplicity Results for Positone Problems. 2.10. General Problems with Sign Changing Nonlinearities. 2.11. Problems with Nonlinear Boundary Data. 2.12. Problems with Mixed Boundary Data. 2.13. Problems with Nonlinear Left Hand Side. 2.14. Infinite Interval Problems I. 2.15. Infinite Interval Problems II. 3: Singular Integral Equations. 3.1. Introduction. 3.2. Nonsingular Integral Equations. 3.3. Singular Integral Equations with a Special Class of Kernels. 3.4. Singular Integral Equations with General Kernels. 3.5. A New Class of Integral Equations. 3.6. Singular and Nonsingular Volterra Integral Equations. Problems. References. Subject Index.

418 pages, Paperback

First published July 31, 2003