Page 14 - Handbook Of Integral Equations

6. Nonlinear Equations With Constant Limits of Integration

6.1. Equations With Quadratic Nonlinearity That Contain Arbitrary Parameters
b

6.1-1. Equations of the Form K(t)y(x)y(t) dt = F(x)
a
b

6.1-2. Equations of the Form G(·· ·) dt = F(x)
a
b
2
6.1-3. Equations of the Form y(x)+ K(x, t)y (t) dt = F(x)
a
b

6.1-4. Equations of the Form y(x)+ K(x, t)y(x)y(t) dt = F(x)
a
b

6.1-5. Equations of the Form y(x)+ G(·· ·) dt = F(x)
a
6.2. Equations With Quadratic Nonlinearity That Contain Arbitrary Functions
b

6.2-1. Equations of the Form G(·· ·) dt = F(x)
a
b
2
6.2-2. Equations of the Form y(x)+ K(x, t)y (t) dt = F(x)
a
b
n m
6.2-3. Equations of the Form y(x)+ K nm (x, t)y (x)y (t) dt = F(x), n + m ≤ 2
a
b

6.2-4. Equations of the Form y(x)+ G(·· ·) dt = F(x)
a
6.3. Equations With Power-Law Nonlinearity
b

6.3-1. Equations of the Form G(·· ·) dt = F(x)
a
b
β
6.3-2. Equations of the Form y(x)+ K(x, t)y (t) dt = F(x)
a
b

6.3-3. Equations of the Form y(x)+ G(·· ·) dt = F(x)
a
6.4. Equations With Exponential Nonlinearity
6.4-1. Integrands With Nonlinearity of the Form exp[βy(t)]
6.4-2. Other Integrands
6.5. Equations With Hyperbolic Nonlinearity
6.5-1. Integrands With Nonlinearity of the Form cosh[βy(t)]
6.5-2. Integrands With Nonlinearity of the Form sinh[βy(t)]
6.5-3. Integrands With Nonlinearity of the Form tanh[βy(t)]
6.5-4. Integrands With Nonlinearity of the Form coth[βy(t)]
6.5-5. Other Integrands
6.6. Equations With Logarithmic Nonlinearity
6.6-1. Integrands With Nonlinearity of the Form ln[βy(t)]
6.6-2. Other Integrands
6.7. Equations With Trigonometric Nonlinearity
6.7-1. Integrands With Nonlinearity of the Form cos[βy(t)]
6.7-2. Integrands With Nonlinearity of the Form sin[βy(t)]
6.7-3. Integrands With Nonlinearity of the Form tan[βy(t)]
6.7-4. Integrands With Nonlinearity of the Form cot[ βy(t)]
6.7-5. Other Integrands
6.8. Equations With Nonlinearity of General Form
b

6.8-1. Equations of the Form G(·· ·) dt = F(x)
a
b

6.8-2. Equations of the Form y(x)+ K(x, t)G y(t) dt = F(x)
a
b

6.8-3. Equations of the Form y(x)+ K(x, t)G t, y(t) dt = F(x)
a
b

6.8-4. Equations of the Form y(x)+ G x, t, y(t) dt = F(x)
a
b

6.8-5. Equations of the Form F x, y(x) + G x, t, y(x), y(t) dt = 0
a
6.8-6. Other Equations
© 1998 by CRC Press LLC
© 1998 by CRC Press LLC
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