Page 413 - Handbook Of Integral Equations

6.4. Equations With Exponential Nonlinearity

6.4-1. Integrands With Nonlinearity of the Form exp[βy(t)]

b

1. y(x)+ A exp[βy(t)] dt = g(x).
a
This is a special case of equation 6.8.27 with f(t, y)= A exp(βy).
b
µ
2. y(x)+ A t exp[βy(t)] dt = g(x).
a
µ
This is a special case of equation 6.8.27 with f(t, y)= At exp(βy).
b

3. y(x)+ A exp µt + βy(t) dt = g(x).
a
This is a special case of equation 6.8.27 with f(t, y)= A exp(µt) exp(βy).
b

4. y(x)+ A exp λ(x – t)+ βy(t) dt = g(x).
a
This is a special case of equation 6.8.28 with f(t, y)= A exp(βy).
b

5. y(x)+ g(x) exp[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.29 with f(t, y) = exp(βy).

b
6. y(x)+ A cosh(λx + µt) exp[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.31 with f(t, y)= A exp(βy).

b
7. y(x)+ A sinh(λx + µt) exp[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.32 with f(t, y)= A exp(βy).

b

8. y(x)+ A cos(λx + µt) exp[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.33 with f(t, y)= A exp(βy).
b

9. y(x)+ A sin(λx + µt) exp[βy(t)] dt = h(x).
a
This is a special case of equation 6.8.34 with f(t, y)= A exp(βy).

6.4-2. Other Integrands

b

10. y(x)+ A exp βy(x)+ γy(t) dt = h(x).
a
This is a special case of equation 6.8.43 with g(x, y)= A exp(βy) and f(t, y) = exp(γy).
b

11. y(x)+ A y(xt) exp[βy(t)] dt =0.
a
This is a special case of equation 6.8.45 with f(t, y)= A exp(βy).

© 1998 by CRC Press LLC

© 1998 by CRC Press LLC
Page 393