| Abstrakt: |
This paper focuses on the following class of fractional magnetic Schrödinger equations: \[ (-\Delta)_{A}^{s}u+V(x)u=g(\vert u\vert^{2})u+\lambda\vert u\vert^{q-2}u, \quad \hbox{in } \mathbb{R}^{N}, \] (− Δ) A s u + V (x) u = g (| u | 2) u + λ | u | q − 2 u , in R N , where $ (-\Delta)_{A}^{s} $ (− Δ) A s is the fractional magnetic Laplacian, $ A :\mathbb {R}^N \rightarrow \mathbb {R}^N $ A : R N → R N is the magnetic potential, $ s\in (0,1) $ s ∈ (0 , 1) , N>2s, $ \lambda \geq 0 $ λ ≥ 0 is a parameter, $ V:\mathbb {R}^N \rightarrow \mathbb {R} $ V : R N → R is a potential function that may decay to zero at infinity and $ g: \mathbb {R}_{+} \rightarrow \mathbb {R} $ g : R + → R is a continuous function with subcritical growth. We deal with supercritical case $ q\geq ~2^*_s:=2N/(N-2s) $ q ≥ 2 s ∗ := 2 N / (N − 2 s). Our approach is based on variational methods combined with penalization technique and $ L^{\infty } $ L ∞ -estimates. [ABSTRACT FROM AUTHOR] |
