Complementary Variational Principles

The book has been mostly rewritten to bring in various improvements
and additions. In particular, the local theory is replaced with a global
treatment based on simple ideas of convexity and monotone operators.
Another major change is that the class of problems treated is much wider
than the Dirichlet type originally discussed. In addition, the variational
results are given a geometrical formulation that includes the hypercircle,
and error estimates for variational solutions are also described.
The number of applications to linear and nonlinear boundary value
problems has been doubled, covering some thirty cases which arise in
mathematical physics, chemistry, engineering, and biology. As well as
containing new derivations of well-known results such as the Rayleigh
and Temple bounds for eigenvalues, the examples contain many results
on upper and lower bounds that have only recently been obtained.
The book is written at a fairly elementary level and should be accessible
to any student with a little knowledge of the calculus of variations and
differential equations.