HANDBOOK OFINTEGRAL EQUATIONS phần 9 potx

... P. Zabreyko, A. I. Koshelev, et al. ( 197 5), F. D. Gakhov ( 197 7), F. G. Tricomi ( 198 5), N. I. Muskhelishvili ( 199 2). Page 645 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC Relations (41) are ... 621 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC 13.3. Complete Singular Integral Equations Solvable in a Closed Form In contrast with characteristic equations and their transposed...

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... second-order linear ordinary differential equations (3) with vari- ous g(x), see E. Kamke ( 197 7), G. M. Murphy ( 196 0), and A. D. Polyanin and V. F. Zaitsev ( 199 5, 199 6). 2 ◦ . Let y 1 = y 1 (x) and y 2 = ... of second-order linear ordinary differential equations (3) with vari- ous f(x), see E. Kamke ( 197 7) and A. D. Polyanin and V. F. Zaitsev ( 199 5, 199 6). 2 ◦ . Let y 1 = y 1...

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... for Supplement 6: G. Doetsch ( 195 0, 195 6, 195 8), H. Bateman and A. Erd ´ elyi ( 195 4), V. A. Ditkin and A. P. Prudnikov ( 196 5). Page 738 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC No Laplace ... x . 44.  dx a 2 + b 2 sin 2 x = 1 a √ a 2 + b 2 arctan √ a 2 + b 2 tan x a . Page 699 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC ... J ν  2 √ ax  11 1 p tanh(ap), a >0 f(...

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... C. Gohberg and M. G. Krein ( 196 7), P. P. Zabreyko, A. I. Koshelev, et al. ( 197 5), A. D. Polyanin and A. V. Manzhirov ( 199 8). Page 577 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC where the ... 580 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC 11 .9. The Carleman Method for Integral Equations of Convolution Type of the Second Kind 11 .9- 1. The Wiener–Hopf Equation of the Seco...

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... Section 9. 2: E. Goursat ( 192 3), H. M. M ¨ untz ( 193 4), A. F. Verlan’ and V. S. Sizikov ( 198 6), A. D. Polyanin and A. V. Manzhirov ( 199 8). Page 463 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC 9. 3-6. ... Section 9. 9: W. V. Lovitt ( 195 0), V. Volterra ( 195 9), S. G. Mikhlin ( 196 0), M. L. Krasnov, A. I. Kiselev, and G. I. Makarenko ( 197 1), V. I. Smirnov ( 197 4). 9. 10....

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... case of equation 6.8. 29 with f(t, y) = coth(βy). Page 396 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC 6.8-4. Equations of the Form y(x)+  b a G  x, t, y(t)  dt = F (x) 39. y(x)+  b a  g 1 (x)f 1  t, ... items 1 ◦ –3 ◦ of equation 6.2.30. Page 413 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC 6.2-2. Equations of the Form y(x)+  b a K(x, t)y 2 (t) dt = F (x) 19. y(x)+...

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... C k can be found by the method of undetermined coefficients. Page 3 29 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC 4 .9- 3. Other Equations of the Form y(x)+  b a K(x, t)y(t) dt = F (x) 26. y(x) ... arccot(βx)]y(t) dt = f(x). This is a special case of equation 4 .9. 10 with h(x) = arccot(βx). Page 293 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC 38. y(x)+  b a sinh(λ|x – t|)g...

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... s 2 . • Reference: P. P. Zabreyko, A. I. Koshelev, et al. ( 197 5). Page 2 29 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC 3.8-2. Equations Containing Modulus 3.  b a |g(x) – g(t)| y(t) dt ... 1.8 .9 with g(x) = cosh(λx). 2.  b a ln   sinh(λx) – sinh(λt)   y(t) dt = f (x). This is a special case of equation 1.8 .9 with g(x) = sinh(λx). Page 226 © 199 8 by CRC Press LLC © 19...

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... – 1 2 ,andn =1,2, • Reference: S. G. Samko, A. A. Kilbas, and O. I. Marichev ( 199 3). Page 90 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC 18.  x a (x – t) ν+1 J ν [λ(x – t)]y(t) dt = f(x). Solution: y(x)=  x a g(t) ... coefficients. The solution can also be obtained by the formula given in 1 .9. 19 (item 3 ◦ ). Page 97 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC 1.6-2. K...

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... the solution of this equation. Page 14 © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC HANDBOOK OF INTEGRAL EQUATIONS © 199 8 by CRC Press LLC © 199 8 by CRC Press LLC 27.  x 0 y(t) dt ax ... Volterra Equations of the 1st Kind 9. 8-1. The First Method 9. 8-2. The Second Method 9. 9. The Successive Approximation Method 9. 9-1. The General Scheme 9. 9-2. A Formula for the...

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