Advanced Nonlinear Studies最新文献_第10页

Asymptotic behavior of solutions to the Monge-Ampère equations with slow convergence rate at infinity 无穷远处慢收敛速度Monge-Ampère方程解的渐近性

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2022-02-14 DOI: 10.1515/ans-2022-0052

Zixiao Liu, J. Bao

引用次数: 0

Existence of two solutions for singular Φ-Laplacian problems 奇异Φ-拉普拉斯问题两个解的存在性

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2022-01-01 DOI: 10.1515/ans-2022-0037

P. Candito, U. Guarnotta, R. Livrea

引用次数: 2

Concentrations for nonlinear Schrödinger equations with magnetic potentials and constant electric potentials 具有磁势和常电位的非线性Schrödinger方程的浓度

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2022-01-01 DOI: 10.1515/ans-2022-0026

Liping Wang, Chunyi Zhao

引用次数: 1

Editorial 编辑

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2022-01-01 DOI: 10.1515/ans-2022-0047

Guozhen Lu

引用次数: 0

Regularity of degenerate k-Hessian equations on closed Hermitian manifolds 闭厄米流形上退化k-Hessian方程的正则性

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2022-01-01 DOI: 10.1515/ans-2022-0025

Dekai Zhang

引用次数: 0

Normalized solutions for a class of scalar field equations involving mixed fractional Laplacians 一类包含混合分数阶拉普拉斯算子的标量场方程的规范化解

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2022-01-01 DOI: 10.1515/ans-2022-0013

Tingjian Luo, H. Hajaiej

引用次数: 10

Multiple solutions to multi-critical Schrödinger equations 多临界Schrödinger方程的多解

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2022-01-01 DOI: 10.1515/ans-2022-0014

Ziyi Xu, Jianfu Yang

{"title":"Multiple solutions to multi-critical Schrödinger equations","authors":"Ziyi Xu, Jianfu Yang","doi":"10.1515/ans-2022-0014","DOIUrl":"https://doi.org/10.1515/ans-2022-0014","url":null,"abstract":"Abstract In this article, we investigate the existence of multiple positive solutions to the following multi-critical Schrödinger equation: (0.1) − Δ u + λ V ( x ) u = μ ∣ u ∣ p − 2 u + ∑ i = 1 k ( ∣ x ∣ − ( N − α i ) ∗ ∣ u ∣ 2 i ∗ ) ∣ u ∣ 2 i ∗ − 2 u in R N , u ∈ H 1 ( R N ) , left{begin{array}{l}-Delta u+lambda Vleft(x)u=mu | u{| }^{p-2}u+mathop{displaystyle sum }limits_{i=1}^{k}left(| x{| }^{-left(N-{alpha }_{i})}ast | u{| }^{{2}_{i}^{ast }})| u{| }^{{2}_{i}^{ast }-2}uhspace{1.0em}hspace{0.1em}text{in}hspace{0.1em}hspace{0.33em}{{mathbb{R}}}^{N},hspace{1.0em} uhspace{0.33em}in {H}^{1}left({{mathbb{R}}}^{N}),hspace{1.0em}end{array}right. where λ , μ ∈ R + , N ≥ 4 lambda ,mu in {{mathbb{R}}}^{+},Nge 4 , and 2 i ∗ = N + α i N − 2 {2}_{i}^{ast }=frac{N+{alpha }_{i}}{N-2} with N − 4 < α i < N N-4lt {alpha }_{i}lt N , i = 1 , 2 , … , k i=1,2,ldots ,k are critical exponents and 2 < p < 2 min ∗ = min { 2 i ∗ : i = 1 , 2 , … , k } 2lt plt {2}_{min }^{ast }={rm{min }}left{{2}_{i}^{ast }:i=1,2,ldots ,kright} . Suppose that Ω = int V − 1 ( 0 ) ⊂ R N Omega ={rm{int}}hspace{0.33em}{V}^{-1}left(0)subset {{mathbb{R}}}^{N} is a bounded domain, we show that for λ lambda large, problem (0.1) possesses at least cat Ω ( Ω ) {{rm{cat}}}_{Omega }left(Omega ) positive solutions.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":"22 1","pages":"273 - 288"},"PeriodicalIF":1.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44038297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Multiplicity and concentration of semi-classical solutions to nonlinear Dirac-Klein-Gordon systems 非线性Dirac-Klein-Gordon系统半经典解的多重性和集中性

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2022-01-01 DOI: 10.1515/ans-2022-0011

Yanheng Ding, Yuanyang Yu, Xiaojing Dong

引用次数: 0

Existence of normalized solutions for the coupled elliptic system with quadratic nonlinearity 二次非线性耦合椭圆系统归一化解的存在性

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2022-01-01 DOI: 10.1515/ans-2022-0010

Jun Wang, Xuan Wang, Song Wei

{"title":"Existence of normalized solutions for the coupled elliptic system with quadratic nonlinearity","authors":"Jun Wang, Xuan Wang, Song Wei","doi":"10.1515/ans-2022-0010","DOIUrl":"https://doi.org/10.1515/ans-2022-0010","url":null,"abstract":"Abstract In the present paper, we study the existence of the normalized solutions for the following coupled elliptic system with quadratic nonlinearity − Δ u − λ 1 u = μ 1 ∣ u ∣ u + β u v in R N , − Δ v − λ 2 v = μ 2 ∣ v ∣ v + β 2 u 2 in R N , left{begin{array}{ll}-Delta u-{lambda }_{1}u={mu }_{1}| u| u+beta uvhspace{1.0em}& hspace{0.1em}text{in}hspace{0.1em}hspace{0.33em}{{mathbb{R}}}^{N}, -Delta v-{lambda }_{2}v={mu }_{2}| v| v+frac{beta }{2}{u}^{2}hspace{1.0em}& hspace{0.1em}text{in}hspace{0.1em}hspace{0.33em}{{mathbb{R}}}^{N},end{array}right. where u , v u,v satisfying the additional condition ∫ R N u 2 d x = a 1 , ∫ R N v 2 d x = a 2 . mathop{int }limits_{{{mathbb{R}}}^{N}}{u}^{2}{rm{d}}x={a}_{1},hspace{1em}mathop{int }limits_{{{mathbb{R}}}^{N}}{v}^{2}{rm{d}}x={a}_{2}. On the one hand, we prove the existence of minimizer for the system with L 2 {L}^{2} -subcritical growth ( N ≤ 3 Nle 3 ). On the other hand, we prove the existence results for different ranges of the coupling parameter β > 0 beta gt 0 with L 2 {L}^{2} -supercritical growth ( N = 5 N=5 ). Our argument is based on the rearrangement techniques and the minimax construction.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":"22 1","pages":"203 - 227"},"PeriodicalIF":1.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49225130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Existence of ground state solutions for critical quasilinear Schrödinger equations with steep potential well 具有陡峭势阱的临界拟线性Schrödinger方程基态解的存在性

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2022-01-01 DOI: 10.1515/ans-2022-0030

Yan-Fang Xue, Xiao-Jing Zhong, Chunlei Tang

引用次数: 2