Ground state solutions for asymptotically periodic Schrödinger-Poisson systems in R^2
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Date
2018-11-27
Authors
Chen, Jing
Chen, Sitong
Tang, Xianhua
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article concerns the planar Schrödinger-Poisson system
-∆u + V(x)u + φu = ƒ(x, u), x ∈ ℝ2,
∆φ = u2, x ∈ ℝ2,
where V(x) and ƒ(x, u) are periodic or asymptotically periodic in x. By combining the variational approach, the non-Nehari manifold approach and new analytic techniques, we establish the existence of ground state solutions for the above problem in the periodic and asymptotically periodic cases. In particular, in our study, ƒ is not required to satisfy the Ambrosetti-Rabinowitz type condition or the Nehari-type monotonic condition.
Description
Keywords
Planar Schrödinger-Poisson system, Ground state solution, Logarithmic convolution potential
Citation
Chen, J., Chen, S., & Tang, X. (2018). Ground state solutions for asymptotically periodic Schrödinger-Poisson systems in R^2. <i>Electronic Journal of Differential Equations, 2018</i>(192), pp. 1-18.
Rights
Attribution 4.0 International