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Some Complementary Bivariational Principles for Linear Integral Equations of Fredholm Type
R. J. Cole and D. C. Pack
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 347, No. 1649 (Dec. 23, 1975), pp. 239-252
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/79108
Page Count: 14
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A simple method is described which can be used to generate complementary bivariational principles yielding upper and lower bounds to the quantity Q = ∫S p(s)n0(s)ds, where p(s) is the (vector) solution of a linear integral equation of Fredholm type p0(s)=p(s)-λ ∫S K(s,s′)p(s′)ds′ and n0(s) and p0(s) are given functions. The method involves a generalization, requiring two approximating functions, of results obtained from a study of the particular case n0(s)=p0(s), a classical variational problem occurring in transport theory and other fields of applied mathematics. The bounds are compared with those of other authors and some further generalizations are indicated.
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences © 1975 Royal Society