Multiple Solutions and Bifurcation for a Class of Nonlinear Sturm-Liouville Eigenvalue Problems on an Unbounded Domain.

Abstract

A class of nonlinear Sturm-Liouville 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)

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1988
Accession Number
ADA195954

Entities

People

  • Chao-nien Chen

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Banach Space
  • Boundary Value Problems
  • Continuous Spectra
  • Differential Equations
  • Eigenvalues
  • Equations
  • Linear Differential Equations
  • Mathematical Analysis
  • Military Research
  • New York
  • Nonlinear Differential Equations
  • Partial Differential Equations
  • Scientific Research
  • Spectra
  • Theorems
  • Variational Methods

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)