Page 18 - Handbook Of Integral Equations

10.6. Dual Integral Equations of the First Kind
10.6-1. The Carleman Method for Equations With Difference Kernels
10.6-2. Exact Solutions of Some Dual Equations of the First Kind
10.6-3. Reduction of Dual Equations to a Fredholm Equation
10.7. Asymptotic Methods for Solving Equations With Logarithmic Singularity
10.7-1. Preliminary Remarks
10.7-2. The Solution for Large λ
10.7-3. The Solution for Small λ
10.7-4. Integral Equation of Elasticity
10.8. Regularization Methods
10.8-1. The Lavrentiev Regularization Method
10.8-2. The Tikhonov Regularization Method

b

11. Methods for Solving Linear Equations of the Form y(x) – K(x, t)y(t) dt = f(x)
a
11.1. Some Definition and Remarks
11.1-1. Fredholm Equations and Equations With Weak Singularity of the 2nd Kind
11.1-2. The Structure of the Solution
11.1-3. Integral Equations of Convolution Type of the Second Kind
11.1-4. Dual Integral Equations of the Second Kind
11.2. Fredholm Equations of the Second Kind With Degenerate Kernel
11.2-1. The Simplest Degenerate Kernel
11.2-2. Degenerate Kernel in the General Case
11.3. Solution as a Power Series in the Parameter. Method of Successive Approximations
11.3-1. Iterated Kernels
11.3-2. Method of Successive Approximations
11.3-3. Construction of the Resolvent
11.3-4. Orthogonal Kernels
11.4. Method of Fredholm Determinants
11.4-1. A Formula for the Resolvent
11.4-2. Recurrent Relations
11.5. Fredholm Theorems and the Fredholm Alternative
11.5-1. Fredholm Theorems
11.5-2. The Fredholm Alternative
11.6. Fredholm Integral Equations of the Second Kind With Symmetric Kernel
11.6-1. Characteristic Values and Eigenfunctions
11.6-2. Bilinear Series
11.6-3. The Hilbert–Schmidt Theorem
11.6-4. Bilinear Series of Iterated Kernels
11.6-5. Solution of the Nonhomogeneous Equation
11.6-6. The Fredholm Alternative for Symmetric Equations
11.6-7. The Resolvent of a Symmetric Kernel
11.6-8. Extremal Properties of Characteristic Values and Eigenfunctions
11.6-9. Integral Equations Reducible to Symmetric Equations
11.6-10. Skew-Symmetric Integral Equations
11.7. An Operator Method for Solving Integral Equations of the Second Kind
11.7-1. The Simplest Scheme
11.7-2. Solution of Equations of the Second Kind on the Semiaxis

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page xviii