Nonlinear Differential Problems with Smooth and Nonsmooth Constraints systematically evaluates how to solve boundary value problems with smooth and nonsmooth constraints. Primarily covering nonlinear elliptic eigenvalue problems and quasilinear elliptic problems using techniques amalgamated from a range of sophisticated nonlinear analysis domains, the work is suitable for PhD and other early career researchers seeking solutions to nonlinear differential equations. Although an advanced work, the book is self-contained, requiring only graduate-level knowledge of functional analysis and topology. Whenever suitable, open problems are stated and partial solutions proposed. The work is accompanied by end-of-chapter problems and carefully curated references.
1. Introduction - p. xv 2. Chapter 1: Elements of Functional Analysis and Operator Theory - p. xvi 3. Chapter 2: Elements of Regularity Theory and Maximum Principle - p. 28 4. Chapter 3: Nonlinear Elliptic Eigenvalue Problems - p. 58 5. Chapter 4: Nonlinear Elliptic Equations with General Dependence on the Gradient of the Solution - p. 139 6. Chapter 5: Constant-Sign and Sign-Changing Solutions for Quasilinear Elliptic Problems - p. 192 7. Chapter 6: Nonlinear Elliptic Systems - p. 228 8. Chapter 7: Singular Quasilinear Elliptic Systems - p. 264 9. Chapter 8: Evolutionary Variational and Quasivariational Inequalities - p. 282 10. Chapter 9: Control Problems for Evolutionary Differential Inclusions - p. 306 11. Bibliography - p. 333 12. Index - p. 343
Nonlinear Differential Problems with Smooth and Nonsmooth Constraints systematically evaluates how to solve boundary value problems with smooth and nonsmooth constraints. Primarily covering nonlinear elliptic eigenvalue problems and quasilinear elliptic problems using techniques amalgamated from a range of sophisticated nonlinear analysis domains, the work is suitable for PhD and other early career researchers seeking solutions to nonlinear differential equations. Although an advanced work, the book is self-contained, requiring only graduate-level knowledge of functional analysis and topology. Whenever suitable, open problems are stated and partial solutions proposed. The work is accompanied by end-of-chapter problems and carefully curated references.
1. Introduction - p. xv 2. Chapter 1: Elements of Functional Analysis and Operator Theory - p. xvi 3. Chapter 2: Elements of Regularity Theory and Maximum Principle - p. 28 4. Chapter 3: Nonlinear Elliptic Eigenvalue Problems - p. 58 5. Chapter 4: Nonlinear Elliptic Equations with General Dependence on the Gradient of the Solution - p. 139 6. Chapter 5: Constant-Sign and Sign-Changing Solutions for Quasilinear Elliptic Problems - p. 192 7. Chapter 6: Nonlinear Elliptic Systems - p. 228 8. Chapter 7: Singular Quasilinear Elliptic Systems - p. 264 9. Chapter 8: Evolutionary Variational and Quasivariational Inequalities - p. 282 10. Chapter 9: Control Problems for Evolutionary Differential Inclusions - p. 306 11. Bibliography - p. 333 12. Index - p. 343
