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List of Symbols
Chapter I. Some Examples to Begin with
Section 1. Various Notations. Linear Equations
Section 2. Nonlinear Equations
Section 3. Nonlinear Systems
Section 4. Further Nonlinear Problems
Section 5. A Free Boundary Problem. The Plate Equation
Chapter II. Introduction
Section 6. Second Order Equations
Section 7. Higher Order Equations
Section 8. Spaces of Continuous Functions. Solution of a Differential Equation
Section 9. Boundary Conditions
Section 10. Solution of a Boundary Value Problem
Section 11. On an Integral Identity
Chapter III. The Weak Solution of a Boundary Value Problem
Section 12. The Carathéodory Property and the Němyckiĭ Operators
Section 13. Sobolev Spaces
Section 14. Differential Operators
Section 15. Boundary Value Problems
Section 16. Various Generalizations
Section 17. Regularity of the Weak Solution
Chapter IV. The Variational Method
Section 18. First Derivative of a Functional
Section 19. Potentials of Boundary Value Problems
Section 20. The Euler Necessary Condition
Section 21. Second Derivative of a Functional
Section 22. Lagrange Conditions
Section 23. Convex Functionals
Section 24. Weak Convergence and Weak Compactness
Section 25. Reflexive Spaces
Section 26. Existence Theorems
Section 27. Minimal Surfaces
Section 28. Excursion on Numerical Methods
Chapter V. The Topological Method
Section 29. Existence Theorems
Section 30. The Brouwer and the Leray-Schauder Degree of a Mapping
Section 31. General Boundary Conditions for Second Order Ordinary Differential Equations
Section 32. Summary of Chapters IV and V. Some Additional Remarks
Chapter VI. Noncoercive Problems
Section 33. Vanishing Nonlinearities. Regular Case
Section 34. Vanishing Nonlinearities. Singular Case
Section 35. Jumping Nonlinearities with Finite Jumps
Section 36. Jumping Nonlinearities with Infinite Jumps
Section 37. Rapid Nonlinearities
Section 38. Periodic Problems
Chapter VII. Variational Inequalities
Section 39. Formulation of the Problem
Section 40. More on the Definition of the Solution of a Variational Inequality
Section 41. Examples
Section 42. Some Special Results
Section 43. Existence Theorems
Studies in Applied Mathematics, 2: Nonlinear Differential Equations focuses on modern methods of solutions to boundary value problems in linear partial differential equations.
The book first tackles linear and nonlinear equations, free boundary problem, second order equations, higher order equations, boundary conditions, and spaces of continuous functions. The text then examines the weak solution of a boundary value problem and variational and topological methods. Discussions focus on general boundary conditions for second order ordinary differential equations, minimal surfaces, existence theorems, potentials of boundary value problems, second derivative of a functional, convex functionals, Lagrange conditions, differential operators, Sobolev spaces, and boundary value problems. The manuscript examines noncoercive problems and vibrational inequalities. Topics include existence theorems, formulation of the problem, vanishing nonlinearities, jumping nonlinearities with finite jumps, rapid nonlinearities, and periodic problems.
The text is highly recommended for mathematicians and engineers interested in nonlinear differential equations.
- No. of pages:
- © Elsevier 1980
- 1st January 1980
- eBook ISBN:
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