Existence and multiplicity of non-trivial solutions for fractional Schrödinger–Poisson systems with a combined nonlinearity
Springer Science and Business Media LLC - Trang 1-14 - 2024
Tóm tắt
In this paper, we are concerned with the following fractional Schrödinger–Poisson system:
$$\begin{aligned} \left\{ \begin{array}{ll} \displaystyle (-\Delta )^s u + V(x)u +\lambda \phi u=K(x){|u|}^ {q-2}u+ f(x,u), &{}\qquad \ x \in \mathbb {R}^3 \\ \displaystyle (-\Delta )^t\phi = u^2,&{} \qquad \ x \in \mathbb {R}^3\\ \end{array}\right. \end{aligned}$$
where
$$\lambda >0$$
is a constant,
$$s,t \in (0,1]$$
,
$$2t+4s>3$$
,
$$1
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