Ground state solutions of Nehari-Pohozaev type for a fractional Schrödinger-Poisson system with critical growth

2020 ◽  
Vol 40 (4) ◽  
pp. 1064-1080
Author(s):  
Wentao Huang ◽  
Li Wang
Keyword(s):  
Ground State ◽  
Critical Growth ◽  
Poisson System ◽  
Ground State Solutions

scholarly journals Multiple positive bound states for critical Schrödinger-Poisson systems

2019 ◽  
Vol 25 ◽  
pp. 73 ◽  
Author(s):  
Giovanna Cerami ◽  
Riccardo Molle
Keyword(s):  
Variational Methods ◽  
Ground State ◽  
Bound States ◽  
Nonlinear Term ◽  
Critical Growth ◽  
Poisson System ◽  
Lack Of Compactness ◽  
Ground State Solutions ◽  
Existence And Multiplicity

Using variational methods we prove some results about existence and multiplicity of positive bound states of to the following Schrödinger-Poisson system: [see formula in PDF] We remark that (SP) exhibits a “double” lack of compactness because of the unboundedness of ℝ3 and the critical growth of the nonlinear term and that in our assumptions ground state solutions of (SP) do not exist.

Ground State Solutions for Quasilinear Schrödinger Equations with Critical Growth and Lower Power Subcritical Perturbation

2019 ◽  
Vol 19 (1) ◽  
pp. 219-237 ◽  
Author(s):  
Yinbin Deng ◽  
Wentao Huang ◽  
Shen Zhang
Keyword(s):  
Ground State ◽  
Nonlinear Function ◽  
Critical Growth ◽  
Quasilinear Schrödinger Equation ◽  
Monotone Method ◽  
Lower Power ◽  
Ground State Solutions ◽  
Change Of Variables ◽  
The Given ◽  
Edinburgh Sect

Abstract We study the following generalized quasilinear Schrödinger equation: -(g^{2}(u)\nabla u)+g(u)g^{\prime}(u)|\nabla u|^{2}+V(x)u=h(u),\quad x\in% \mathbb{R}^{N}, where {N\geq 3} , {g\colon\mathbb{R}\rightarrow\mathbb{R}^{+}} is an even differentiable function such that {g^{\prime}(t)\geq 0} for all {t\geq 0} , {h\in C^{1}(\mathbb{R},\mathbb{R})} is a nonlinear function including critical growth and lower power subcritical perturbation, and the potential {V(x)\colon\mathbb{R}^{N}\rightarrow\mathbb{R}} is positive. Since the subcritical perturbation does not satisfy the (AR) condition, the standard variational method cannot be used directly. Combining the change of variables and the monotone method developed by Jeanjean in [L. Jeanjean, On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on {\mathbf{R}}^{N} , Proc. Roy. Soc. Edinburgh Sect. A 129 1999, 4, 787–809], we obtain the existence of positive ground state solutions for the given problem.

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