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.
|Number of pages||12|
|Journal||Dynamic Systems and Applications|
|Publication status||Published - Jun 1 2013|
- Principle of symmetric criticality
- Schrödinger equation
- Three-critical points theorem
ASJC Scopus subject areas