%0 Journal Article
%A
%A
%T Some complementary bivariational principles for linear integral equations of Fredholm type
%D 1975
%R 10.1098/rspa.1975.0207
%J Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
%P 239-252
%V 347
%N 1649
%X A simple method is described which can be used to generate complementary 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) — λ ∫sK(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.
%U http://rspa.royalsocietypublishing.org/content/royprsa/347/1649/239.full.pdf