Summary and Info
The book has been mostly rewritten to bring in various improvementsand additions. In particular, the local theory is replaced with a globaltreatment based on simple ideas of convexity and monotone operators.Another major change is that the class of problems treated is much widerthan the Dirichlet type originally discussed. In addition, the variationalresults 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 valueproblems has been doubled, covering some thirty cases which arise inmathematical physics, chemistry, engineering, and biology. As well ascontaining new derivations of well-known results such as the Rayleighand Temple bounds for eigenvalues, the examples contain many resultson upper and lower bounds that have only recently been obtained.The book is written at a fairly elementary level and should be accessibleto any student with a little knowledge of the calculus of variations anddifferential equations.
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