Accession Number : ADA136404

Title :   Applications of Natural Constraints in Critical Point Theory to Boundary Value Problems on Domains with Rotation Symmetry.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : VAN Groesen,E W C

PDF Url : ADA136404

Report Date : Nov 1983

Pagination or Media Count : 27

Abstract : In this paper a nonlinear Dirichlet problem for the Laplace operator is considered on a disc in R sub 2. It is shown that if the nonlinearity, which may explicitly depend on the radial variable, is odd and superlinear at infinity, there exist infinitely many non-radial solutions. If the nonlinearity is odd and sublinear at infinity, and satisfies certain conditions at zero, a finite number of radial and non-radial solutions will be found. This number is given by the number of radial, respectively non-radial, eigenvalues that are crossed by the nonlinearity. In any case, as a consequence of the oddness of the nonlinearity, these solutions inherit the nodal line structure of the eigenfunctions corresponding to the eigenvalues that are crossed. The results are obtained by using natural constraints in a variational approach of the problem. (Author)

Descriptors :   *Problem solving, *Boundary value problems, *Nonlinear analysis, Variational methods, Equations, Eigenvalues, Rotation, Symmetry, Eigenvectors

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE