Minimax principles for the solution of semilinear gradient operator equations in hilbert space.
A new variational characterization of solutions for an important class of nonlinear operator equations is obtained. The result obtained is used to derive sharp necessary and sufficient conditions for the solvability of such operator equations. Examples of the applicability of the results obtained to nonlinear Dirichlet problems and global differential geometry are discussed.
The Institute for Advanced Study, Princeton, New Jersey 08540.
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MS
Berger