Some Variational Principles for Integral Equations

摘要: Complementary variational principles are developed for the solution of Fredholm integral equations with symmetric positive‐definite kernels. In particular, theory is applied to linear type φ(r)=f(r)+λ∫K(r,s)φ(s)ds, and bounds obtained ∫fφdr. When λ negative, complementary upper lower ones. positive, one‐sided, but an improvement made on a result Strieder Prager [J. Math. Phys. 8, 514 (1967)]. A condition given by these authors existence does not seem be strictly necessary, alternative conditions derived. Systematic iterative scaling procedures discussed.