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

@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 -