Fractional Schrödinger-Poisson system with critical growth and potentials vanishing at infinity. (English) Zbl 1529.35563
The authors in this paper consider a fractional elliptic problem in \(\mathbb{R}^3\) involving a (fractional) Schrödinger equation coupled with the (fractional) Poisson equation. The equation possesses competing potentials which may decay and vanish at infinity and a critical nonlinearity perturbed by a subcritical one. The authors are interested in finding positive solutions as well as their decay rate at infinity.
The problem is addressed by variational methods, using minimax techniques, penalization methods and Concentration Compactness Principle to recover the compactness.
Under some local conditions, the existence and concentration of positive solutions, as well its polynomial decay is proved.
The problem is addressed by variational methods, using minimax techniques, penalization methods and Concentration Compactness Principle to recover the compactness.
Under some local conditions, the existence and concentration of positive solutions, as well its polynomial decay is proved.
Reviewer: Gaetano Siciliano (São Paulo)
MSC:
| 35R11 | Fractional partial differential equations |
| 35B35 | Stability in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 92C17 | Cell movement (chemotaxis, etc.) |
| 35J47 | Second-order elliptic systems |
Keywords:
concentration-compactness principle; critical exponents; decaying potentials; fractional Schrödinger-Poisson system; positive solutionsReferences:
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