Discrete boundary value problems involving oscillatory nonlinearities: Small and large solutions

Alexandru Kristály, Mihai Mihǎilescu, Vicenţiu Rǎdulescu

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

We consider the discrete boundary value problem (P): -Δ(Δu(k - 1)) = f(u(k)), k ∈ [1,T], u(0) = u(T + 1) = 0, where the nonlinear termf: [0, ∞) → ℝ has an oscillatory behaviour near the origin or at infinity. By a direct variational method, we show that (P) has a sequence of non-negative, distinct solutions which converges to 0 (respectively +∞) in the sup-norm wheneverfoscillates at the origin (respectively at infinity).

Original languageEnglish
Pages (from-to)1431-1440
Number of pages10
JournalJournal of Difference Equations and Applications
Volume17
Issue number10
DOIs
Publication statusPublished - Oct 1 2011

Keywords

  • Difference equations
  • Large solutions
  • Oscillatory nonlinearities
  • Small solutions

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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