| Abstrakt: |
We consider the following class of elliptic problems \[ - \Delta_A u + u = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u ,\quad x\in {\mathbb{R}}^N, \] − Δ A u + u = a λ (x) | u | q − 2 u + b μ (x) | u | p − 2 u , x ∈ R N , where $ 1 1 < q < 2 < p < 2 ∗ = 2 N N − 2 $ N\geq ~3 $ N ≥ 3 , $ a_{\lambda }(x) $ a λ (x) is a sign-changing weight function, $ b_{\mu }(x) $ b μ (x) is continuous, $ \lambda > 0 $ λ > 0 and $ \mu > 0 $ μ > 0 are real parameters, $ u \in H^1_A({\mathbb {R}}^N) $ u ∈ H A 1 ( R N) and $ A:{\mathbb {R}}^N \rightarrow {\mathbb {R}}^N $ A : R N → R N is a magnetic potential. Exploring the relationship between the Nehari manifold and fibering maps, we will discuss the existence, multiplicity and regularity of solutions. [ABSTRACT FROM AUTHOR] |
