### 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 |
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Pages (from-to) | 325-336 |

Number of pages | 12 |

Journal | Dynamic Systems and Applications |

Volume | 22 |

Issue number | 2-3 |

Publication status | Published - 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)

### Cite this

*Dynamic Systems and Applications*,

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