A dimension-depending multiplicity result for a perturbed schrödinger equation

Alexandru Kristály, Gheorghe Moroçanu, Donal O'Regan

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4 Citations (Scopus)

Abstract

We consider the Schrödinger equation for equation where N ≥ 2, λ,μ ≥ 0 are parameters, V, K, L : RN→ R are radially symmetric potentials, f : R → R is a continuous function with sublinear growth at infinity, and g : R → R is a continuous sub-critical function. We first prove that for A small enough no non-zero solution exists for (Pλ,0), while for λ large and μ small enough at least two distinct non-zero radially symmetric solutions do exist for (P λμ). By exploiting a Ricceri-type three-critical points theorem, the principle of symmetric criticality and a group-theoretical approach, the existence of at least N - 3 (N mod 2) distinct pairs of non-zero solutions is guaranteed for (Pλμ) whenever A is large and λ is small enough, N 3, and /, g are odd.

Original languageEnglish
Pages (from-to)325-336
Number of pages12
JournalDynamic Systems and Applications
Volume22
Issue number2-3
Publication statusPublished - Jun 1 2013

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Keywords

  • Principle of symmetric criticality
  • Schrödinger equation
  • Sublinear
  • Three-critical points theorem

ASJC Scopus subject areas

  • Mathematics(all)

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