On the existence of nontrivial solutions for modified fractional Schrödinger-Poisson systems via perturbation method

Atefe Goli; Sayyed Hashem Rasouli; Somayeh Khademloo

Applications of Mathematics (2025)

  • Issue: 2, page 293-310
  • ISSN: 0862-7940

Abstract

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The existence of nontrivial solutions is considered for the fractional Schrödinger-Poisson system with double quasi-linear terms: ( - Δ ) s u + V ( x ) u + φ u - 1 2 u ( - Δ ) s u 2 = f ( x , u ) , x 3 , ( - Δ ) t φ = u 2 , x 3 , where ( - Δ ) α is the fractional Laplacian for α = s , t ( 0 , 1 ] with s < t and 2 t + 4 s > 3 . Under assumptions on V and f , we prove the existence of positive solutions and negative solutions for the above system by using perturbation method and the mountain pass theorem.

How to cite

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Goli, Atefe, Rasouli, Sayyed Hashem, and Khademloo, Somayeh. "On the existence of nontrivial solutions for modified fractional Schrödinger-Poisson systems via perturbation method." Applications of Mathematics (2025): 293-310. <http://eudml.org/doc/299978>.

@article{Goli2025,
abstract = {The existence of nontrivial solutions is considered for the fractional Schrödinger-Poisson system with double quasi-linear terms: \[ \{\left\lbrace \begin\{array\}\{ll\} (-\Delta )^\{s\}u+V(x)u+\phi u -\{1\over 2\}u (-\Delta )^\{s\}u^\{2\}=f(x,u), & x\in \mathbb \{R\}^\{3\} ,\\ (-\Delta )^\{t\} \phi = u^\{2\}, & x\in \mathbb \{R\}^\{3\}, \end\{array\}\right.\} \] where $(-\Delta )^\{\alpha \}$ is the fractional Laplacian for $\alpha =s$, $t\in (0,1]$ with $s<t$ and $2t+4s>3$. Under assumptions on $V$ and $f$, we prove the existence of positive solutions and negative solutions for the above system by using perturbation method and the mountain pass theorem.},
author = {Goli, Atefe, Rasouli, Sayyed Hashem, Khademloo, Somayeh},
journal = {Applications of Mathematics},
keywords = {fractional-Schrödinger-Poisson; quasi-linear term; perturbation method; variational method},
language = {eng},
number = {2},
pages = {293-310},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the existence of nontrivial solutions for modified fractional Schrödinger-Poisson systems via perturbation method},
url = {http://eudml.org/doc/299978},
year = {2025},
}

TY - JOUR
AU - Goli, Atefe
AU - Rasouli, Sayyed Hashem
AU - Khademloo, Somayeh
TI - On the existence of nontrivial solutions for modified fractional Schrödinger-Poisson systems via perturbation method
JO - Applications of Mathematics
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 2
SP - 293
EP - 310
AB - The existence of nontrivial solutions is considered for the fractional Schrödinger-Poisson system with double quasi-linear terms: \[ {\left\lbrace \begin{array}{ll} (-\Delta )^{s}u+V(x)u+\phi u -{1\over 2}u (-\Delta )^{s}u^{2}=f(x,u), & x\in \mathbb {R}^{3} ,\\ (-\Delta )^{t} \phi = u^{2}, & x\in \mathbb {R}^{3}, \end{array}\right.} \] where $(-\Delta )^{\alpha }$ is the fractional Laplacian for $\alpha =s$, $t\in (0,1]$ with $s<t$ and $2t+4s>3$. Under assumptions on $V$ and $f$, we prove the existence of positive solutions and negative solutions for the above system by using perturbation method and the mountain pass theorem.
LA - eng
KW - fractional-Schrödinger-Poisson; quasi-linear term; perturbation method; variational method
UR - http://eudml.org/doc/299978
ER -

References

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