One-dimensional scalar field equations involving an oscillatory nonlinear term

Francesca Faraci, Alexandru Kristály

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this paper we study the equation -u″+V(x)u = W(x)f(u), x ∈ ℝ, where the nonlinear term f has certain oscillatory behaviour. Via two different variational arguments, we show the existence of infinitely many homoclinic solutions whose norms in an appropriate functional space which involves the potential V tend to zero (resp. at infinity) whenever f oscillates at zero (resp. at infinity). Unlike in classical results, neither symmetry property on f nor periodicity on the potentials V and W are required.

Original languageEnglish
Pages (from-to)107-120
Number of pages14
JournalDiscrete and Continuous Dynamical Systems
Volume18
Issue number1
DOIs
Publication statusPublished - May 2007

Keywords

  • Infinitely solutions
  • Oscillatory nonlinearity
  • Scalar field equation

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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