We consider the logarithmic elliptic equation with singular nonlinearity {Δu+ulogu^(2)+λ/u^(γ)=0,in Ω,u>0,in Ω,u=0,on δΩ,where Ω⊂R^(N)(N≥3)is a bounded domain with a smooth boundary,0<γ<1 andλis a ...We consider the logarithmic elliptic equation with singular nonlinearity {Δu+ulogu^(2)+λ/u^(γ)=0,in Ω,u>0,in Ω,u=0,on δΩ,where Ω⊂R^(N)(N≥3)is a bounded domain with a smooth boundary,0<γ<1 andλis a positive constant.By using a variational method and the critical point theory for a nonsmooth functional,we obtain the existence of two positive solutions.This result generalizes and improves upon recent results in the literature.展开更多
This article concerns the existence of multi-bump positive solutions for the following logarithmic Schrödinger equation:{−Δu+λV(x)u=ulogu^(2)inRN,u∈H^(1)(R^(N)),where N≥1,⋋>0 is a parameter and the nonnega...This article concerns the existence of multi-bump positive solutions for the following logarithmic Schrödinger equation:{−Δu+λV(x)u=ulogu^(2)inRN,u∈H^(1)(R^(N)),where N≥1,⋋>0 is a parameter and the nonnegative continuous function V:ℝ^(N)→ℝhas potential wellΩ:=int V^(−1)(0)which possesses k disjoint bounded componentsΩ=∪^(k)_(j)=1Ω_(j).Using the variational methods,we prove that if the parameter⋋>0 is large enough,then the equation has at least 2^(k)−1 multi-bump positive solutions.展开更多
基金supported by Natural Science Foundation of Guizhou Minzu University(20185773-YB03)supported by Fundamental Research Funds of China West Normal University(18B015)+2 种基金Innovative Research Team of China West Normal University(CXTD2018-8)supported by National Natural Science Foundation of China(11861021)supported by National Natural Science Foundation of China(11661021)。
文摘We consider the logarithmic elliptic equation with singular nonlinearity {Δu+ulogu^(2)+λ/u^(γ)=0,in Ω,u>0,in Ω,u=0,on δΩ,where Ω⊂R^(N)(N≥3)is a bounded domain with a smooth boundary,0<γ<1 andλis a positive constant.By using a variational method and the critical point theory for a nonsmooth functional,we obtain the existence of two positive solutions.This result generalizes and improves upon recent results in the literature.
基金supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq/Brazil(Grant No.304804/2017-7)supported by Natural Science Foundation of Shanghai(Grant Nos.20ZR1413900 and 18ZR1409100)。
文摘This article concerns the existence of multi-bump positive solutions for the following logarithmic Schrödinger equation:{−Δu+λV(x)u=ulogu^(2)inRN,u∈H^(1)(R^(N)),where N≥1,⋋>0 is a parameter and the nonnegative continuous function V:ℝ^(N)→ℝhas potential wellΩ:=int V^(−1)(0)which possesses k disjoint bounded componentsΩ=∪^(k)_(j)=1Ω_(j).Using the variational methods,we prove that if the parameter⋋>0 is large enough,then the equation has at least 2^(k)−1 multi-bump positive solutions.
