DECAY PROPERTIES AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS FOR THE NONLINEAR FRACTIONAL SCHRÖDINGER-POISSON SYSTEM

Lintao Liu; Haibo Chen; Jie Yang

doi:10.11948/20220378

2023 Volume 13 Issue 6

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(6): 3136-3157

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Lintao Liu, Haibo Chen, Jie Yang. DECAY PROPERTIES AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS FOR THE NONLINEAR FRACTIONAL SCHRÖDINGER-POISSON SYSTEM[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3136-3157. doi: 10.11948/20220378

Citation:

Lintao Liu, Haibo Chen, Jie Yang. DECAY PROPERTIES AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS FOR THE NONLINEAR FRACTIONAL SCHRÖDINGER-POISSON SYSTEM[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3136-3157. doi: 10.11948/20220378

DECAY PROPERTIES AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS FOR THE NONLINEAR FRACTIONAL SCHRÖDINGER-POISSON SYSTEM

1.
School of Mathematics and Statistics, Central South University, 410083 Changsha, China
2.
School of Mathematics and Computational Science, Huaihua University, 418008 Huaihua, China

Author Bio: Email: liulintao1995@163.com(L. Liu); Email: dafeyang@163.com(J. Yang)
Corresponding author: Email: math_chb@163.com(H. Chen)

Abstract

Abstract

In this paper, we study the following nonlinear fractional Schrödinger-Poisson system
$\begin{equation*}\left\{\begin{array}{ll}(-\Delta)^{s}u+\lambda V(x)u+\mu\phi u=|u|^{p-2}u, & \hbox{in}\; \mathbb{R}^3 , \\(-\Delta)^{s}\phi=u^{2}, & \hbox{in}\; \mathbb{R}^3, \end{array}\right.\end{equation*}$
where $s\in(\frac{3}{4}, 1)$, $ 2<p<4$, $\lambda, \mu$ are positive parameters and the potential $V(x)$ is a nonnegative continuous function with a potential well $\Omega=int V^{-1}(0)$. By establishing truncation technique and the parameter-dependent compactness lemma, the existence, decay rate and asymptotic behavior of positive solutions are established. Moreover, we prove some nonexistence results in the case of $ 2<p\leq3$.
- Fractional Schrödinger-Poisson system /
- positive solutions /
- truncation technique /
- steep potential well
MSC: 35J50, 35J20

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References

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