Accession Number : AD0690556

Title :   A SHARP SUFFICIENT CONDITION FOR SOLUTION OF A NONLINEAR ELLIPTIC BOUNDARY VALUE PROBLEM,

Corporate Author : CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS

Personal Author(s) : Williams,S.

Report Date : 1969

Pagination or Media Count : 11

Abstract : The paper establishes a sufficient condition such that the equation Au + g(u) = h has a weak solution u with generalized Dirichlet data zero where A is any self-adjoint strongly and uniformly elliptic linear partial differential operator with real-valued, reasonably smooth coefficients defined on a bounded open set Omega of E superscript n, where h is square-integrable and real-valued on Omega, and where g is any continuous real-valued function defined for all real numbers such that g(infinity) = lim as x approaches infinity g(x) and g(minus infinity) = lim as x approaches minus infinity g(x) exist (and are finite) such that g(minus infinity) = or < g(x) = or < g(infinity) for all real x. (Author)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, *BOUNDARY VALUE PROBLEMS), NONLINEAR DIFFERENTIAL EQUATIONS, MEASURE THEORY, BANACH SPACE

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE