On sublinear fractional Schrödinger–Poisson systems

Abderrazek Benhassine ()
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Abderrazek Benhassine: University of Monastir

Partial Differential Equations and Applications, 2021, vol. 2, issue 3, 1-13

Abstract: Abstract We look for solutions to a sublinear fractional Schrödinger–Poisson system $$\begin{aligned} (-\Delta )^s u+V(x)u+K(x)\phi u=f(x,u),\quad x\in {\mathbb {R}}^3,\\ (-\Delta )^t\phi =K(x)u^2,\quad x\in {\mathbb {R}}^3, \end{aligned}$$ ( - Δ ) s u + V ( x ) u + K ( x ) ϕ u = f ( x , u ) , x ∈ R 3 , ( - Δ ) t ϕ = K ( x ) u 2 , x ∈ R 3 , where $$(-\Delta )^\alpha $$ ( - Δ ) α denotes the fractional Laplacian of order $$\alpha \in (0,1).$$ α ∈ ( 0 , 1 ) . Applying a new symmetric mountain pass theorem established by Kajikia, we prove the existence of infinitely many solutions for the above equations under certain assumptions on $$V,\ K$$ V , K and f. Some examples are also given to illustrate our main theoretical result.

Keywords: Fractional Schrödinger equations; Critical point theory; Symmetric mountain pass theorem; 49J35; 35Q40; 81V10 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00103-w

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