Radial ground state sign-changing solutions for a class of asymptotically cubic or super-cubic Schrödinger–Poisson type problems

2018 ◽  
Vol 113 (2) ◽  
pp. 627-643 ◽  
Author(s):  
Sitong Chen ◽  
Xianhua Tang
Keyword(s):  
Ground State ◽  
Sign Changing Solutions ◽  
Asymptotically Cubic ◽  
Poisson Type

scholarly journals Sign-changing solutions for a Schrödinger–Kirchhoff–Poisson system with 4-sublinear growth nonlinearity

2021 ◽  
pp. 1-21
Author(s):  
Shubin Yu ◽  
Ziheng Zhang ◽  
Rong Yuan
Keyword(s):  
Type System ◽  
Invariant Sets ◽  
Smooth Domain ◽  
Positive Parameter ◽  
Poisson System ◽  
Bounded Smooth Domain ◽  
Existence And Multiplicity ◽  
Bounded Smooth ◽  
Sign Changing Solutions ◽  
Poisson Type

In this paper we consider the following Schrödinger–Kirchhoff–Poisson-type system { − ( a + b ∫ Ω | ∇ u | 2 d x ) Δ u + λ ϕ u = Q ( x ) | u | p − 2 u in   Ω , − Δ ϕ = u 2 in   Ω , u = ϕ = 0 on   ∂ Ω , where Ω is a bounded smooth domain of R 3 , a > 0 , b ≥ 0 are constants and λ is a positive parameter. Under suitable conditions on Q ( x ) and combining the method of invariant sets of descending flow, we establish the existence and multiplicity of sign-changing solutions to this problem for the case that 2 < p < 4 as λ sufficient small. Furthermore, for λ = 1 and the above assumptions on Q ( x ) , we obtain the same conclusions with 2 < p < 12 5 .

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