On the Existence of Ground State Solutions for Fractional Schrödinger–Poisson Systems with General Potentials and Super-quadratic Nonlinearity
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DOI: 10.1007/s00009-018-1179-8
Abstract: In this article, we are concerned with the following fractional Schrödinger–Poisson system: $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s}u+V(x)u+\phi u=f(u)&{} \quad \hbox {in}~\mathbb {R}^{3},\\ (-\Delta )^{t}\phi =u^2&{} \quad \hbox {in}~\mathbb {R}^{3},\\ \end{array} \right. \end{aligned}$$(-Δ)su+V(x)u+ϕu=f(u)inR3,(-Δ)tϕ=u2inR3,where $$03$$2s+2t>3, and $$f\in… read more here.
Keywords: dinger poisson; fractional schr; state solutions; ground state ... See more keywords
Existence of Ground State Solutions for Fractional Schrödinger–Poisson Systems with Doubly Critical Growth
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DOI: 10.1007/s00009-020-01660-x
Abstract: This paper considers a class of fractional Schrodinger–Poisson type systems with doubly critical growth $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^su+V(x)u-\phi |u|^{2^*_s-3}u=K(x)|u|^{2^*_s-2}u,&{} \text{ in } {\mathbb {R}}^3,\\ (-\Delta )^s\phi =|u|^{2^*_s-1},&{} \text{ in } {\mathbb {R}}^3, \end{array}\right. \end{aligned}$$… read more here.
Keywords: ground state; systems doubly; doubly critical; state solutions ... See more keywords
Existence of ground state solutions of Nehari-Pankov type to Schrödinger systems
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DOI: 10.1007/s11425-017-9332-3
Abstract: This paper is dedicated to studying the following elliptic system of Hamiltonian type: $$\begin{cases}-\varepsilon^2\Delta{u}+u+V(x)v=Q(x)F_v{(u,v)}, & x \in \mathbb{R}^N,\\-\varepsilon^2\Delta{v}+v+V(x)u=Q(x)F_u{(u,v)}, & x \in \mathbb{R}^N,\\|u(x)|+|v(x)|\rightarrow0, & as |x|\rightarrow \infty\end{cases}$$ { − ε 2 Δ u + u +… read more here.
Keywords: nehari pankov; pankov type; mathbb; type ... See more keywords
Existence of ground state solutions to Hamiltonian elliptic system with potentials
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DOI: 10.1016/s0252-9602(18)30859-2
Abstract: Abstract In this paper, we investigate nonlinear Hamiltonian elliptic system { ( - Δ ) u = b → ( x ) ⋅ ∇ u + ( V ( x ) + τ ) u… read more here.
Keywords: hamiltonian elliptic; elliptic system; state solutions; ground state ... See more keywords