Large Nonlinearities and Closedness.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Alternative theorems for nonlinear equations of the form Lx Nx 0 in a Banach space X are obtained, thereby reducing the solution of such problems to alternative problems in proper subspaces. Here L is closed and DN belongs to DL but otherwise both L and N are generally unbounded and possess no special compactness or positivity properties. A graph norm depending on a parameter and the closedness of L are employed to control the size and type of nonlinearities that can be permitted. Also included are some applications of these results to semilinear elliptic boundary value problems, and some observations which relate the closedness of L to existence of pseudo-inverses, boundedness of projections, and splittings in the case of the residual spectrum. Author
- Theoretical Mathematics