### Abstract

We consider the Schrödinger equation for equation where N ≥ 2, λ,μ ≥ 0 are parameters, V, K, L : R^{N}→ 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 (P_{λ},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 (P_{λμ}) whenever A is large and λ is small enough, N 3, and /, g are odd.

Original language | English |
---|---|

Pages (from-to) | 325-336 |

Number of pages | 12 |

Journal | Dynamic Systems and Applications |

Volume | 22 |

Issue number | 2-3 |

Publication status | Published - Jun 2013 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Dynamic Systems and Applications*,

*22*(2-3), 325-336.

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

Research output: Contribution to journal › Article

*Dynamic Systems and Applications*, vol. 22, no. 2-3, pp. 325-336.

}

TY - JOUR

T1 - A dimension-depending multiplicity result for a perturbed schrödinger equation

AU - Kristály, A.

AU - Moroçanu, Gheorghe

AU - O'Regan, Donal

PY - 2013/6

Y1 - 2013/6

N2 - 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.

AB - 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.

KW - Principle of symmetric criticality

KW - Schrödinger equation

KW - Sublinear

KW - Three-critical points theorem

UR - http://www.scopus.com/inward/record.url?scp=84880490471&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880490471&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84880490471

VL - 22

SP - 325

EP - 336

JO - Dynamic Systems and Applications

JF - Dynamic Systems and Applications

SN - 1056-2176

IS - 2-3

ER -