Page 13 - Handbook Of Integral Equations

4.7-5. Kernels Containing Hyperbolic and Trigonometric Functions
4.7-6. Kernels Containing Logarithmic and Trigonometric Functions
4.8. Equations Whose Kernels Contain Special Functions
4.8-1. Kernels Containing Bessel Functions
4.8-2. Kernels Containing Modified Bessel Functions
4.9. Equations Whose Kernels Contain Arbitrary Functions
4.9-1. Equations With Degenerate Kernel: K(x, t)= g 1 (x)h 1 (t)+ ·· · + g n (x)h n (t)
4.9-2. Equations With Difference Kernel: K(x, t)= K(x – t)
b

4.9-3. Other Equations of the Form y(x)+ K(x, t)y(t) dt = F(x)
a
b

4.9-4. Equations of the Form y(x)+ K(x, t)y(·· ·) dt = F(x)
a
4.10. Some Formulas and Transformations
5. Nonlinear Equations With Variable Limit of Integration
5.1. Equations With Quadratic Nonlinearity That Contain Arbitrary Parameters
x
5.1-1. Equations of the Form y(t)y(x – t) dt = F(x)
x
0
5.1-2. Equations of the Form K(x, t)y(t)y(x – t) dt = F(x)
x
0
5.1-3. Equations of the Form G(·· ·) dt = F(x)
0
x 2
5.1-4. Equations of the Form y(x)+ K(x, t)y (t) dt = F(x)
x
a
5.1-5. Equations of the Form y(x)+ K(x, t)y(t)y(x – t) dt = F(x)
a
5.2. Equations With Quadratic Nonlinearity That Contain Arbitrary Functions
x

5.2-1. Equations of the Form G(·· ·) dt = F(x)
a
x 2
5.2-2. Equations of the Form y(x)+ K(x, t)y (t) dt = F(x)
x
a
5.2-3. Equations of the Form y(x)+ G(·· ·) dt = F(x)
a
5.3. Equations With Power-Law Nonlinearity
5.3-1. Equations Containing Arbitrary Parameters
5.3-2. Equations Containing Arbitrary Functions
5.4. Equations With Exponential Nonlinearity
5.4-1. Equations Containing Arbitrary Parameters
5.4-2. Equations Containing Arbitrary Functions
5.5. Equations With Hyperbolic Nonlinearity
5.5-1. Integrands With Nonlinearity of the Form cosh[βy(t)]
5.5-2. Integrands With Nonlinearity of the Form sinh[βy(t)]
5.5-3. Integrands With Nonlinearity of the Form tanh[βy(t)]
5.5-4. Integrands With Nonlinearity of the Form coth[βy(t)]
5.6. Equations With Logarithmic Nonlinearity
5.6-1. Integrands Containing Power-Law Functions of x and t
5.6-2. Integrands Containing Exponential Functions of x and t
5.6-3. Other Integrands
5.7. Equations With Trigonometric Nonlinearity
5.7-1. Integrands With Nonlinearity of the Form cos[βy(t)]
5.7-2. Integrands With Nonlinearity of the Form sin[βy(t)]
5.7-3. Integrands With Nonlinearity of the Form tan[βy(t)]
5.7-4. Integrands With Nonlinearity of the Form cot[ βy(t)]
5.8. Equations With Nonlinearity of General Form
x

5.8-1. Equations of the Form G(·· ·) dt = F(x)
a
x
5.8-2. Equations of the Form y(x)+ K(x, t)G y(t) dt = F(x)
x
a
5.8-3. Equations of the Form y(x)+ K(x, t)G t, y(t) dt = F(x)
a
5.8-4. Other Equations
© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page xiii