Existence and multiplicity results for nonlinear Schrödinger-Poisson equation with general potential

doi:10.1007/s11464-020-0881-6

Front. Math. China

2020, Vol. 15

Issue (6) : 1189-1200 https://doi.org/10.1007/s11464-020-0881-6

RESEARCH ARTICLE

Existence and multiplicity results for nonlinear Schrödinger-Poisson equation with general potential

Yuan SHAN(

)

School of Statistics and Mathematics, Nanjing Audit University, Nanjing 210029, China

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Abstract

This paper is concerned with the Schrödinger-Poisson equation $− Δ u + V (x) u + φ (x) u = f (x, u), x ∈ ℝ 3,$ $− Δ φ = u 2, lim ⁡ | x | → + ∞ φ (x) = 0.$

Under certain hypotheses on V and a general spectral assumption, the existence and multiplicity of solutions are obtained via variational methods.

Keywords Schrdinger-Poisson equation Morse index variational method

Corresponding Author(s): Yuan SHAN

Issue Date: 05 February 2021

Cite this article:

Yuan SHAN. Existence and multiplicity results for nonlinear Schrödinger-Poisson equation with general potential[J]. Front. Math. China, 2020, 15(6): 1189-1200.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0881-6
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I6/1189

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