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 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.
