Accession Number : AD0696326

Title :   BRANCHING OF SOLUTIONS OF AN EQUATION IN HILBERT SPACE.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Sather,D.

Report Date : MAY 1969

Pagination or Media Count : 34

Abstract : A constructive method is developed to study the branching of solutions of the equation (I - lambda L)w + T(w) = nu p in a (real) Hilbert space H(lambda and nu are real parameters). The operator L is linear selfadjoint and compact, and the nonlinear operator T maps a neighborhood of the origin in H into H and is homogeneous of (integral) degree k(k = or > 2). The approach is based on the Lyapunov-Schmidt method and does not require that the nonlinear operator T be compact. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, THEOREMS), PARTIAL DIFFERENTIAL EQUATIONS, INTEGRAL EQUATIONS, OPERATORS(MATHEMATICS), HILBERT SPACE, MATRICES(MATHEMATICS), NONLINEAR SYSTEMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE