Existence of Forced Oscillations for Some Nonlinear Differential Equations.

Abstract

This article studies the existence of T-periodic solutions for systems of nonlinear second order ordinary differential equations. Assuming function V to be superquadratic, it is shown that this system possesses infinitely many T-periodic solutions. The proof of this result rests on showing that certain homotopy groups of level sets of the functional associated with the system are not trivial. Some more general results concerning systems of another type are also presented.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1982
Accession Number
ADA124372

Entities

People

  • Abbas Bahri
  • Henri Berestycki

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Autonomous Systems
  • Boundary Value Problems
  • Differential Equations
  • Eigenvalues
  • Equations
  • Formulas (Mathematics)
  • Functional Analysis
  • Hilbert Space
  • Mathematics
  • Nonlinear Differential Equations
  • Partial Differential Equations
  • Periodic Functions
  • Polynomials
  • Sequences
  • United States
  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.