This monograph presents an up to date account of the literature on singular problems. One of our aims also is to present recent theory on singular differential and integral equations to a new and wider audience. The book presents a compact, thorough, and self-contained account for singular problems. An important feature of this book is that we illustrate how easily the theory can be applied to discuss many real world examples of current interest.
|Edition description:||Softcover reprint of hardcover 1st ed. 2003|
|Product dimensions:||6.10(w) x 9.25(h) x 0.03(d)|
Table of Contents
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.