
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 UNIVMADISON 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 nonradial solutions. If the nonlinearity is odd and sublinear at infinity, and satisfies certain conditions at zero, a finite number of radial and nonradial solutions will be found. This number is given by the number of radial, respectively nonradial, 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