检索结果-南通市图书馆

Acta Mathematicae Applicatae Sinica 2022年第2期38卷 463-483页

作者： Na LI Xiao-ming HE College of Science Minzu University of ChinaBeijing 100081China

In this paper,we study the existence of positive solution for the p-laplacian equations with frac-tional critical nonlinearity{-Δ)_(p)^(s)u+V(x)|u|^(p-2)u=K(x)f(u)+p(x)|u|p_(s)^(*)-^(2)u,x∈R^(N),u∈Ds,p(RN),where s∈(0,1),p_(s)^(*)=Np/N-sp,N>sp,p>1 and V(x),K(x)are positive continuous functions which vanish at infinity,f is a function with a subcritical growth,and p(x)is bounded,nonnegative continuous function.By using variational method in the weighted spaces,we prove the above problem has at least one positive solution.

关键词： fractional p-laplacian Variational methods Mountain pass Theorem Critical growth Vanishing potential

The Brezis–Nirenberg problem for the fractional p-laplacian in Unbounded Domains

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2023年第11期39卷 2181-2206页

作者： Yan Sheng SHEN School of Mathematical Sciences Jiangsu UniversityZhenjiang 212013P.R.China

In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains.By means of the fractional poincaréinequality in unbounded cylindrical domains,we first study the asymptotic property of the first eigenvalueλp,s(ωδ)with respect to the domainωδ.Then,by applying the concentration-compactness principle for fractional Sobolev spaces in unbounded domains,we prove the existence results.The present work complements the results of Mosconi–perera–Squassina–Yang[The Brezis–Nirenberg problem for the fractional p-laplacian.C alc.Var.partial Differential Equations,55(4),25 pp.2016]to unbounded domains and extends the classical Brezis–Nirenberg type results of Ramos–Wang–Willem[positive solutions for elliptic equations with critical growth in unbounded domains.In:Chapman Hall/CRC press,Boca Raton,2000,192–199]to the fractional p-laplacian setting.

关键词： Brezis–Nirenberg problem fractional poincaréinequality fractional p-laplacian unbounded cylinder type domains concentration–compactness principle

Infinitely Many Solutions for Schrödinger–Choquard–Kirchhoff Equations Involving the fractional p-laplacian

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2021年第2期37卷 315-332页

作者： Li WANG Tao HAN Ji Xiu WANG College of Science East China Jiaotong UniversityNanchang 330013P.R.China School of Mathematics and Statistics Hubei University of Arts and ScienceXiangyang 441053P.R.China

In this article,we show the existence of infinitely many solutions for the fractional p-laplacian equations of Schrödinger–Kirchhoff type equation M([u]_(s,p)^(p))(−Δ)_(p)^(s)u+V(x)|u|^(p−2)u=λ(Iα∗|u|^(p_(s,α)^(∗)))|u|^(p_(s,α)^(∗)−2)u+βk(x)|u|^(q−2)u,x∈R^(N),where(−Δ)s p is the fractional p-laplacian operator,[u]s,p is the Gagliardo p-seminorm,0ppositive functions,and k(x)is a non-negative function in an appropriate Lebesgue space.Combining the concentration-compactness principle in fractional Sobolev space and Kajikiya’s new version of the symmetric mountain pass lemma,we obtain the existence of infinitely many solutions which tend to zero for suitable positive parameters λ and β.

关键词： Schrödinger–Choquard–Kirchhoff type fractional p-laplacian variational methods critical Sobolev exponent

Symmetry and monotonicity of positive solutions to Schr?dinger systems with fractional p-laplacians

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 2022年第1期37卷 52-72页

作者： MA Ling-wei ZHANG Zhen-qiu School of Mathematical Sciences Tianjin Normal UniversityTianjin 300387China School of Mathematical Sciences and LpMC Nankai UniversityTianjin 300071China

In this paper,we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-laplacian systems.By virtue of this method,we investigate the qualitative properties of positive solutions for the following Schrodinger system with fractional p-laplacian{(-△)^(s)_(p)u+au^(p-1)=f(u,v),(-△)^(t)_(p)v+bv(p-1)=g(u,v),where 0ppace R^(N)(N≥2),the monotonicity in the parabolic domain and the nonexistence on the half space for positive solutions to the above system under some suitable conditions on f and g,respectively.

关键词： fractional p-laplacian Schr?dinger systems direct method of moving planes radial symmetry monotonicity nonexistence