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Akademický článek

Existence and asymptotic behaviour of positive ground state solution for critical Schrödinger-Bopp-Podolsky system

Autor: Senli Liu, Haibo Chen

Publikováno v: Electronic Research Archive, Vol 30, Iss 6, Pp 2138-2164 (2022)

In this paper, we consider a class of critical Schrödinger-Bopp-Podolsky system. By virtue of the Nehari manifold and variational methods, we study the existence, nonexistence and asymptotic behavior of ground state solutions for this problem.

Externí odkaz: https://doaj.org/article/a25668b3bf2f43549e041948d7836129

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Akademický článek

Schrodinger-Poisson systems with singular potential and critical exponent

Autor: Senli Liu, Haibo Chen, Zhaosheng Feng

Publikováno v: Electronic Journal of Differential Equations, Vol 2020, Iss 130,, Pp 1-17 (2020)

In this article we study the Schrodinger-Poisson system $$\displaylines{ -\Delta u +V(|x|)u+\lambda\phi u = f(u), \quad x\in\mathbb{R}^3, \cr -\Delta \phi =u^2, \quad x\in\mathbb{R}^3, }$$ where V is a singular potential with the parameter $\alp

Externí odkaz: https://doaj.org/article/ee5e7e084ba449feb70d9d04f4036625

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Akademický článek

The existence of nontrivial solution of a class of Schrödinger–Bopp–Podolsky system with critical growth

Autor: Jie Yang, Haibo Chen, Senli Liu

Publikováno v: Boundary Value Problems, Vol 2020, Iss 1, Pp 1-16 (2020)

Abstract We consider the following Schrödinger–Bopp–Podolsky problem: { − Δ u + V ( x ) u + ϕ u = λ f ( u ) + | u | 4 u , in R 3 , − Δ ϕ + Δ 2 ϕ = u 2 , in R 3 . $$ \textstyle\begin{cases} -\Delta u+V(x) u+\phi u=\lambda f(u)+ \vert u

Externí odkaz: https://doaj.org/article/8a60dced20f645e5bc974b9409411367

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Akademický článek

Fractional Schrodinger-Poisson systems with weighted Hardy potential and critical exponent

Autor: Yu Su, Haibo Chen, Senli Liu, Xianwen Fang

Publikováno v: Electronic Journal of Differential Equations, Vol 2020, Iss 01,, Pp 1-17 (2020)

In this article we consider the fractional Schrodinger-Poisson system $$\displaylines{ (-\Delta)^{s} u - \mu \frac{\Phi(x/|x|)}{|x|^{2s}} u +\lambda \phi u = |u|^{2^*_s-2}u,\quad \text{in } \mathbb{R}^3,\cr (-\Delta)^t \phi = u^2, \quad \text{in

Externí odkaz: https://doaj.org/article/ec96bfe3b0ba4af3b8785510f9cd248b

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Akademický článek

Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems

Autor: Jie Yang, Haibo Chen, Senli Liu

Publikováno v: Advances in Mathematical Physics, Vol 2020 (2020)

We consider the following double phase problem with variable exponents: −div∇upx−2∇u+ax∇uqx−2∇u=λfx,u in Ω,u=0, on ∂Ω. By using the mountain pass theorem, we get the existence results of weak solutions for the aforementioned proble

Externí odkaz: https://doaj.org/article/3b1f0f5d60014292b7ac351820cf2efb

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Akademický článek

Multiplicity of Nodal Solutions for a Class of Double-Phase Problems

Autor: Jie Yang, Haibo Chen, Senli Liu

Publikováno v: Journal of Function Spaces, Vol 2020 (2020)

We consider the following parametric double-phase problem: −div∇up−2∇u+ax∇uq−2∇u=λfx,u in Ω,u=0,on ∂Ω.. We do not impose any global growth conditions to the nonlinearity fx,u, which refer solely to its behavior in a neighborhood of

Externí odkaz: https://doaj.org/article/4040687526f6417a8480af81a740b534

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