@article {Cole239,
author = { and },
title = {Some complementary bivariational principles for linear integral equations of Fredholm type},
volume = {347},
number = {1649},
pages = {239--252},
year = {1975},
doi = {10.1098/rspa.1975.0207},
publisher = {The Royal Society},
abstract = {A simple method is described which can be used to generate complemen-tary bivariational principles yielding upper and lower bounds to the quantity Q = ∫sp(s) n0(s) ds, where p(s) is the (vector) solution of a linear integral equation of Fredholm type p0(s) = p(s) {\textemdash} λ ∫sK(s, s{\textquoteright}) p(s{\textquoteright}) ds{\textquoteright} and n0(s) and p0(s) are given functions. The method involves a generaliza-tion, 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.},
issn = {0080-4630},
URL = {http://rspa.royalsocietypublishing.org/content/347/1649/239},
eprint = {http://rspa.royalsocietypublishing.org/content/347/1649/239.full.pdf},
journal = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences}
}