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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
1204 BOUNDARY VALUE PROBLEMS. GREENS FUNCTION
2
. Distinct eigenfunctions y
n
(x) and y
m
(x) are orthogonal with weight s(x) on the inter-
val x
1
x x
2
:
Z
x
2
x
1
s(x)y
n
(x)y
m
(x) dx = 0 for n 6= m.
3
. If the conditions
q(x) 0, α
1
β
1
0, α
2
β
2
0 (17.1.2.5)
are satisfied, there are no negative eigenvalues. If q 0 and β
1
= β
2
= 0, then λ
1
= 0
is the least eigenvalue, with the corresponding eigenfunction ϕ
1
= const . Otherwise, all
eigenvalues are positive, provided that conditions (17.1.2.5) are satisfied.
Other general and special properties of the Sturm–Liouville problem (17.1.2.4) are
given in Section 3.8.9; various asymptotic and approximate formulas for the ...
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Publisher Resources

ISBN: 9781466581494