In this paper, by using the method of moving planes, we are concerned with the symmetry and monotonicity of positive solutions for the fractional Hartree equation.
In this paper,we study the existence of localized nodal solutions for Schrodinger-Poisson systems with critical growth{−ε^(2)Δv+V(x)v+λψv=v^(5)+μ|v|^(q−2)v,in R^(3),−ε^(2)Δψ=v^(2),in R^(3);v(x)→0,ψ(x)→0as|x...In this paper,we study the existence of localized nodal solutions for Schrodinger-Poisson systems with critical growth{−ε^(2)Δv+V(x)v+λψv=v^(5)+μ|v|^(q−2)v,in R^(3),−ε^(2)Δψ=v^(2),in R^(3);v(x)→0,ψ(x)→0as|x|→∞.We establish,for smallε,the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function via the perturbation method,and employ some new analytical skills to overcome the obstacles caused by the nonlocal term φu(x)=1/4π∫R^(3)u^(2)(y)/|x−y|dy.Our results improve and extend related ones in the literature.展开更多
In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation --Δpu=f（x）u^-α ＋ λg（x）u^β in RN, where N ≥3, 1 〈 p 〈 N, λ〉 0, 0 〈 α〈 1,max（p, ...In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation --Δpu=f（x）u^-α ＋ λg（x）u^β in RN, where N ≥3, 1 〈 p 〈 N, λ〉 0, 0 〈 α〈 1,max（p, 2） 〈 β＋ 1 〈 p＊ = Np/N-p We prove that there exists a critical value A such that the problem has at least two solutions if 0 〈 λ 〈 A; at least one solution if λ= A; and no solutions if λ〉A.展开更多
The existence of an infinite sequence of sign-changing solutions are proved for a class of quasilinear elliptic equations under suitable conditions on the quasilinear coefficients and the nonlinearity ■on aΩ ,where...The existence of an infinite sequence of sign-changing solutions are proved for a class of quasilinear elliptic equations under suitable conditions on the quasilinear coefficients and the nonlinearity ■on aΩ ,where Ω∈ C RN is a bounded domain with smooth boundary,and we use du 2u d D;u=x,Dju=;dxjdxj and D2bj;(z)=;bj(2).The main interest of this paper is for the case of bounded quasilinearity bj.The result is proved by an elliptic regularization method involving truncations of both u and the gradient of u.展开更多
基金supported by NSFC(11761082)Yunnan Province,Young Academic and Technical Leaders Program(2015HB028)
文摘In this paper, by using the method of moving planes, we are concerned with the symmetry and monotonicity of positive solutions for the fractional Hartree equation.
文摘In this paper,we study the existence of localized nodal solutions for Schrodinger-Poisson systems with critical growth{−ε^(2)Δv+V(x)v+λψv=v^(5)+μ|v|^(q−2)v,in R^(3),−ε^(2)Δψ=v^(2),in R^(3);v(x)→0,ψ(x)→0as|x|→∞.We establish,for smallε,the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function via the perturbation method,and employ some new analytical skills to overcome the obstacles caused by the nonlocal term φu(x)=1/4π∫R^(3)u^(2)(y)/|x−y|dy.Our results improve and extend related ones in the literature.
基金supported by Natural Science Foundation of China under Grant No. 10871110
文摘In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation --Δpu=f（x）u^-α ＋ λg（x）u^β in RN, where N ≥3, 1 〈 p 〈 N, λ〉 0, 0 〈 α〈 1,max（p, 2） 〈 β＋ 1 〈 p＊ = Np/N-p We prove that there exists a critical value A such that the problem has at least two solutions if 0 〈 λ 〈 A; at least one solution if λ= A; and no solutions if λ〉A.
基金The authors would like to thank the referee for carefully reading the paper and for helpful suggestions.The work is partially supported by NSFC(Nos.11761082,11671364,11771324 and 11831009).
文摘The existence of an infinite sequence of sign-changing solutions are proved for a class of quasilinear elliptic equations under suitable conditions on the quasilinear coefficients and the nonlinearity ■on aΩ ,where Ω∈ C RN is a bounded domain with smooth boundary,and we use du 2u d D;u=x,Dju=;dxjdxj and D2bj;(z)=;bj(2).The main interest of this paper is for the case of bounded quasilinearity bj.The result is proved by an elliptic regularization method involving truncations of both u and the gradient of u.
