
Accession Number : ADA195954
Title : Multiple Solutions and Bifurcation for a Class of Nonlinear SturmLiouville Eigenvalue Problems on an Unbounded Domain.
Descriptive Note : Technical Summary rept.,
Corporate Author : WISCONSIN UNIVMADISON CENTER FOR MATHEMATICAL SCIENCES
Personal Author(s) : Chen, ChaoNien
PDF Url : ADA195954
Report Date : Apr 1988
Pagination or Media Count : 129
Abstract : A class of nonlinear SturmLiouville problems is considered. These problems admit zero as a trivial solution and the nonlinear operator linearized about zero has a purely continuous spectrum 0, INFINITY). Variational methods and approximation arguments are used to obtain the existence of nontrivial solutions with any prescribed number of nodes and for some nonlinearities it is shown that this solution is unique. Moreover, the lowest point of the continuous spectrum is bifurcation point; infinitely many continua of solutions, which are distinguished by nodal properties, bifurcate from the line of trivial solutions at this point. Results are also obtained in higher dimensions via investigation of the set of radial solutions of appropriate partial differential equations. Keywords: Nodes; Ordinary differential equations; Boundary value problems. (KR)
Descriptors : *EIGENVALUES, *NONLINEAR ANALYSIS, BOUNDARY VALUE PROBLEMS, CONTINUOUS SPECTRA, DIFFERENTIAL EQUATIONS, NODES, NONLINEAR SYSTEMS, OPERATORS(PERSONNEL), PARTIAL DIFFERENTIAL EQUATIONS, SOLUTIONS(GENERAL), VARIATIONAL METHODS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE