We prove the existence of a ground state positive solution of Schrödinger-Poisson systems in the plane of the form where p≥4, γ, b>0 and the potential V is assumed to be positive and unbounded at infinity. On the potential we do not require any symmetry or periodicity assumption, and it is not supposed it has a limit at infinity. We approach the problem by variational methods, using a variant of the mountain pass theorem and the Cerami compactness condition.
Molle, R., Sardilli, A. (2022). On a planar Schrödinger-Poisson system involving a non-symmetric potential. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 65(4), 1133-1146 [10.1017/S0013091522000517].
On a planar Schrödinger-Poisson system involving a non-symmetric potential
Molle R.
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2022-01-01
Abstract
We prove the existence of a ground state positive solution of Schrödinger-Poisson systems in the plane of the form where p≥4, γ, b>0 and the potential V is assumed to be positive and unbounded at infinity. On the potential we do not require any symmetry or periodicity assumption, and it is not supposed it has a limit at infinity. We approach the problem by variational methods, using a variant of the mountain pass theorem and the Cerami compactness condition.| File | Dimensione | Formato | |
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