A dimension-depending multiplicity result for a perturbed schrödinger equation

A. Kristály, Gheorghe Moroçanu, Donal O'Regan

Research output: Contribution to journalArticle

2 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 2013

Fingerprint

Multiplicity Results
Distinct
Radially Symmetric Solutions
Criticality
Critical point
Continuous Function
Odd
Infinity
Theorem

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A dimension-depending multiplicity result for a perturbed schrödinger equation. / Kristály, A.; Moroçanu, Gheorghe; O'Regan, Donal.

In: Dynamic Systems and Applications, Vol. 22, No. 2-3, 06.2013, p. 325-336.

Research output: Contribution to journalArticle

Kristály, A. ; Moroçanu, Gheorghe ; O'Regan, Donal. / A dimension-depending multiplicity result for a perturbed schrödinger equation. In: Dynamic Systems and Applications. 2013 ; Vol. 22, No. 2-3. pp. 325-336.
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