Author | Piccinini, L. C. author |
---|---|
Title | Ordinary Differential Equations in Rn [electronic resource] : Problems and Methods / by L. C. Piccinini, G. Stampacchia, G. Vidossich |
Imprint | New York, NY : Springer New York, 1984 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5188-0 |
Descript | XII, 385 p. online resource |
I Existence and Uniqueness for the Initial Value Problem Under the Hypothesis of Lipschitz -- 1. General Results -- 2. Qualitative Properties of Solutions -- 3. Solutions as Functions of the Initial Data -- 4. Systems of Equations as Particular Transformations Between Function Spaces -- 5. Exercises -- 6. Bibliographical Notes -- II Linear Systems -- 1. Elements of Linear Algebra -- 2. Linear Systems of Ordinary Differential Equations -- 3. Operational Calculus -- 4. Linear Finite Differences Equations -- 5. Examples -- 6. Bibliography -- III Existence and Uniqueness for the Cauchy Problem Under the Condition of Continuity -- 1. Existence Theorem -- 2. The Peano Phenomenon -- 3. Questions of Uniqueness -- 4. Elements of G-Convergence -- 5. Bibliographical Notes -- IV Boundary Value Problems -- 1. Continuous Mappings on Euclidean Spaces -- 2. Geometric Boundary Value Problems -- 3. Sturm-Liouvilie Problems: Eigenvalues and Existence and Uniqueness Theorems -- 4. Periodic Solutions -- 5. Functional Boundary Value Problems -- 6. Bibliographical Notes -- V Questions of Stability -- 1. Stability of the Solutions of Linear Systems -- 2. Some Methods for the Determination of the Stability of Nonlinear Systems -- 3. Some Applications -- 4. The Method of Runge and Kutta -- 5. Bibliographical Notes