Accession Number : AD0761863

Title :   Large Nonlinearities and Closedness.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Gustafson,K. ; Sather,D.

Report Date : APR 1973

Pagination or Media Count : 25

Abstract : Alternative theorems for nonlinear equations of the form Lx + N(x) = 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 D(N) belongs to D(L) 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)

Descriptors :   (*NONLINEAR DIFFERENTIAL EQUATIONS, FUNCTIONAL ANALYSIS), BANACH SPACE, MAPPING(TRANSFORMATIONS), PARTIAL DIFFERENTIAL EQUATIONS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE