Advances in Nonlinear Analysis最新文献_第10页

Spectral discretization of the time-dependent Navier-Stokes problem with mixed boundary conditions 混合边界条件下含时Navier-Stokes问题的谱离散化

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0253

M. Abdelwahed, N. Chorfi

引用次数: 4

On the singularly perturbation fractional Kirchhoff equations: Critical case 奇异摄动分数阶Kirchhoff方程的临界情形

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0234

Guangze Gu, Zhipeng Yang

{"title":"On the singularly perturbation fractional Kirchhoff equations: Critical case","authors":"Guangze Gu, Zhipeng Yang","doi":"10.1515/anona-2022-0234","DOIUrl":"https://doi.org/10.1515/anona-2022-0234","url":null,"abstract":"Abstract This article deals with the following fractional Kirchhoff problem with critical exponent a + b ∫ R N ∣ ( − Δ ) s 2 u ∣ 2 d x ( − Δ ) s u = ( 1 + ε K ( x ) ) u 2 s ∗ − 1 , in R N , left(a+bmathop{int }limits_{{{mathbb{R}}}^{N}}| {left(-Delta )}^{tfrac{s}{2}}uhspace{-0.25em}{| }^{2}{rm{d}}xright){left(-Delta )}^{s}u=left(1+varepsilon Kleft(x)){u}^{{2}_{s}^{ast }-1},hspace{1.0em}hspace{0.1em}text{in}hspace{0.1em}hspace{0.33em}{{mathbb{R}}}^{N}, where a , b > 0 a,bgt 0 are given constants, ε varepsilon is a small parameter, 2 s ∗ = 2 N N − 2 s {2}_{s}^{ast }=frac{2N}{N-2s} with 0 < s < 1 0lt slt 1 and N ≥ 4 s Nge 4s . We first prove the nondegeneracy of positive solutions when ε = 0 varepsilon =0 . In particular, we prove that uniqueness breaks down for dimensions N > 4 s Ngt 4s , i.e., we show that there exist two nondegenerate positive solutions which seem to be completely different from the result of the fractional Schrödinger equation or the low-dimensional fractional Kirchhoff equation. Using the finite-dimensional reduction method and perturbed arguments, we also obtain the existence of positive solutions to the singular perturbation problems for ε varepsilon small.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45264734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 14

Existence and concentration of ground-states for fractional Choquard equation with indefinite potential 具有不定势的分数阶Choquard方程基态的存在与集中

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0255

Wen Zhang, Shuai Yuan, Lixi Wen

引用次数: 24

Application of Capacities to Space-Time Fractional Dissipative Equations II: Carleson Measure Characterization for Lq(ℝ+n+1,μ) L^q (mathbb{R}_ + ^{n + 1} ,mu ) −Extension 容量在时空分数耗散方程中的应用Ⅱ：Lq的Carleson测度表征(ℝ+n+1，μ）L^q（mathbb{R}_+^｛n+1｝，mu）−扩展

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2021-0232

Pengtao Li, Zhichun Zhai

引用次数: 2

Lower and upper estimates of semi-global and global solutions to mixed-type functional differential equations 混合型泛函微分方程半全局解和全局解的上下估计

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2021-0218

J. Diblík, G. Vážanová

引用次数: 2

A class of hyperbolic variational–hemivariational inequalities without damping terms 一类不含阻尼项的双曲变分-半变分不等式

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0237

Shengda Zeng, S. Migórski, V. T. Nguyen

引用次数: 2

Optimal decay rate for higher–order derivatives of solution to the 3D compressible quantum magnetohydrodynamic model 三维可压缩量子磁流体力学模型解的高阶导数的最优衰减率

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2021-0219

Juan Wang, Yinghui Zhang

{"title":"Optimal decay rate for higher–order derivatives of solution to the 3D compressible quantum magnetohydrodynamic model","authors":"Juan Wang, Yinghui Zhang","doi":"10.1515/anona-2021-0219","DOIUrl":"https://doi.org/10.1515/anona-2021-0219","url":null,"abstract":"Abstract We investigate optimal decay rates for higher–order spatial derivatives of strong solutions to the 3D Cauchy problem of the compressible viscous quantum magnetohydrodynamic model in the H5 × H4 × H4 framework, and the main novelty of this work is three–fold: First, we show that fourth order spatial derivative of the solution converges to zero at the L2-rate (1+t)-114 {L^2} - {rm{rate}},{(1 + t)^{- {{11} over 4}}} , which is same as one of the heat equation, and particularly faster than the L2-rate (1+t)-54 {L^2} - {rm{rate}},{(1 + t)^{- {5 over 4}}} in Pu–Xu [Z. Angew. Math. Phys., 68:1, 2017] and the L2-rate (1+t)-94 {L^2} - {rm{rate}},{(1 + t)^{- {9 over 4}}} , in Xi–Pu–Guo [Z. Angew. Math. Phys., 70:1, 2019]. Second, we prove that fifth–order spatial derivative of density ρ converges to zero at the L2-rate (1+t)-134 {L^2} - {rm{rate}},{(1 + t)^{- {{13} over 4}}} , which is same as that of the heat equation, and particularly faster than ones of Pu–Xu [Z. Angew. Math. Phys., 68:1, 2017] and Xi–Pu–Guo [Z. Angew. Math. Phys., 70:1, 2019]. Third, we show that the high-frequency part of the fourth order spatial derivatives of the velocity u and magnetic B converge to zero at the L2-rate (1+t)-134 {L^2} - {rm{rate}},{(1 + t)^{- {{13} over 4}}} , which are faster than ones of themselves, and totally new as compared to Pu–Xu [Z. Angew. Math. Phys., 68:1, 2017] and Xi–Pu–Guo [Z. Angew. Math. Phys., 70:1, 2019].","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42280589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 2

Centered Hardy-Littlewood maximal function on product manifolds 乘积流形上的中心Hardy-Littlewood极大函数

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2021-0233

Shiliang Zhao

引用次数: 0

Bounded solutions to systems of fractional discrete equations 分数阶离散方程系统的有界解

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2022-0260

J. Diblík

{"title":"Bounded solutions to systems of fractional discrete equations","authors":"J. Diblík","doi":"10.1515/anona-2022-0260","DOIUrl":"https://doi.org/10.1515/anona-2022-0260","url":null,"abstract":"Abstract The article is concerned with systems of fractional discrete equations Δ α x ( n + 1 ) = F n ( n , x ( n ) , x ( n − 1 ) , … , x ( n 0 ) ) , n = n 0 , n 0 + 1 , … , {Delta }^{alpha }xleft(n+1)={F}_{n}left(n,xleft(n),xleft(n-1),ldots ,xleft({n}_{0})),hspace{1em}n={n}_{0},{n}_{0}+1,ldots , where n 0 ∈ Z {n}_{0}in {mathbb{Z}} , n n is an independent variable, Δ α {Delta }^{alpha } is an α alpha -order fractional difference, α ∈ R alpha in {mathbb{R}} , F n : { n } × R n − n 0 + 1 → R s {F}_{n}:left{nright}times {{mathbb{R}}}^{n-{n}_{0}+1}to {{mathbb{R}}}^{s} , s ⩾ 1 sgeqslant 1 is a fixed integer, and x : { n 0 , n 0 + 1 , … } → R s x:left{{n}_{0},{n}_{0}+1,ldots right}to {{mathbb{R}}}^{s} is a dependent (unknown) variable. A retract principle is used to prove the existence of solutions with graphs remaining in a given domain for every n ⩾ n 0 ngeqslant {n}_{0} , which then serves as a basis for further proving the existence of bounded solutions to a linear nonhomogeneous system of discrete equations Δ α x ( n + 1 ) = A ( n ) x ( n ) + δ ( n ) , n = n 0 , n 0 + 1 , … , {Delta }^{alpha }xleft(n+1)=Aleft(n)xleft(n)+delta left(n),hspace{1em}n={n}_{0},{n}_{0}+1,ldots , where A ( n ) Aleft(n) is a square matrix and δ ( n ) delta left(n) is a vector function. Illustrative examples accompany the statements derived, possible generalizations are discussed, and open problems for future research are formulated as well.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45448471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 6

Thresholds for the existence of solutions to inhomogeneous elliptic equations with general exponential nonlinearity 具有一般指数非线性的非齐次椭圆型方程解存在性的阈值

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI: 10.1515/anona-2021-0220

Kazuhiro Ishige, S. Okabe, Tokushi Sato

引用次数: 2