دانلود کتاب Generalized Inverse Operators: And Fredholm Boundary-Value Problems

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Contents\nPreface\nPreface to the second edition\nNotation\nChapter\r1. Preliminary Information\n 1.1 Metric and Normed Spaces\n 1.2 Hilbert Spaces\n 1.3 Banach Spaces\n 1.4 Linear Operators\n 1.5 Unilateral Inverse, Generalized Inverse, and Pseudoinverse Operators\nChapter\r2. Generalized Inverse Operators in Banach Spaces\n 2.1 Finite-Dimensional Operators\n 2.2 An Analog of the Schmidt Lemma for Fredholm Operators\n 2.3 Generalized Inverse Operators for Bounded Linear Fredholm Operators\n 2.4 Generalized Inverse Matrices\nChapter\r3. Pseudoinverse Operators in Hilbert Spaces\n 3.1 Orthoprojectors, Their Properties, and Relation to Finite-Dimensional Operators\n 3.2 An Analog of the Schmidt Lemma for Fredholm Operators\n 3.3 Left and Right Pseudoinverse Operators for Bounded Linear Fredholm Operators\n 3.4 Pseudoinverse Operators for Bounded Linear Fredholm Operators\n 3.5 Inverse Operators for Fredholm Operators of Index Zero\n 3.6 Criterion of Solvability and the Representation of Solutions of Fredholm Linear Operator Equations\n 3.7 Integral Fredholm Equations with Degenerate Kernels in the Critical Cases\n 3.8 Pseudoinverse Matrices\n 4. Boundary-Value Problems for Operator Equations\n 4.1 Linear Boundary-Value Problems for Fredholm Operator Equations\n 4.2 Generalized Green Operator\n 4.3 Examples\nChapter\r5. Boundary-Value Problems for Systems of Ordinary Differential Equations\n 5.1 Linear Boundary-Value Problems. Criterion of Solvability\n 5.2 Weakly Nonlinear Boundary-Value Problems\n 5.3 Autonomous Boundary-Value Problems\n 5.4 General Scheme of Investigation of the Boundary-Value Problems\n 5.5 Periodic Solutions of the Mathieu, Riccati, and Van der Pol Equations\n 5.6 Differential Systems with Delay\n 5.7 Fredholm Boundary-Value Problems for Differential Systems with Single Delay\n 5.8 Degenerate Systems of Ordinary Differential Equations\nChapter\r6. Impulsive Boundary-Value Problems for Systems of Ordinary Differential Equations\n 6.1 Linear Boundary-Value Problems. Criterion of Solvability\n 6.2 Generalized Green Operator for the Semihomogeneous Boundary-Value Problem and Its Properties\n 6.3 Regularization of Linear Impulsive Boundary-Value Problems\n 6.4 Conditions for the Appearance of Solutions of Weakly Perturbed Linear Boundary-Value Problems\n 6.5 Weakly Nonlinear Boundary-Value Problems\n 6.6 Critical Case. Necessary Condition for the Existence of Solutions\n 6.7 Sufficient Condition for the Existence of Solutions. Iterative Algorithm for the Construction of Solutions\n 6.8 Critical Case of the Second Order\n 6.9 Degenerate Systems of Differential Equations with Impulsive Action\nChapter\r7. Solutions of Differential and Difference Systems Bounded on the Entire Real Axis\n 7.1 Solutions of Linear Weakly Perturbed Systems Bounded on the Entire Real Axis\n 7.2 Nonlinear Systems\n 7.3 Solutions of Linear and Nonlinear Difference Equations Bounded on the Entire Real Axis\nEpilogue\nBibliography