Advances in Nonlinear Analysis最新文献_第7页

High energy solutions of general Kirchhoff type equations without the Ambrosetti-Rabinowitz type condition 不含Ambrosetti-Rabinowitz型条件的一般Kirchhoff型方程的高能解

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0311

Jian Zhang, Hui Liu, J. Zuo

引用次数: 4

Positive solutions for a class of singular (p, q)-equations 一类奇异(p, q)方程的正解

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0300

S. Leonardi, Nikolaos S. Papageorgiou

引用次数: 1

Dynamical analysis of a reaction–diffusion mosquito-borne model in a spatially heterogeneous environment 空间异质环境下反应-扩散蚊媒模式的动力学分析

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0295

Jinliang Wang, W. Wu, Chunyang Li

引用次数: 1

Fujita-type theorems for a quasilinear parabolic differential inequality with weighted nonlocal source term 具有加权非局部源项的拟线性抛物型微分不等式的Fujita型定理

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0303

Yuepeng Li, Z. Fang

引用次数: 1

Uniform decay estimates for the semi-linear wave equation with locally distributed mixed-type damping via arbitrary local viscoelastic versus frictional dissipative effects 基于任意局部粘弹性与摩擦耗散效应的具有局部分布混合阻尼的半线性波动方程的一致衰减估计

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2023-01-01 DOI: 10.1515/anona-2022-0285

Kun‐Peng Jin, Li Wang

{"title":"Uniform decay estimates for the semi-linear wave equation with locally distributed mixed-type damping via arbitrary local viscoelastic versus frictional dissipative effects","authors":"Kun‐Peng Jin, Li Wang","doi":"10.1515/anona-2022-0285","DOIUrl":"https://doi.org/10.1515/anona-2022-0285","url":null,"abstract":"Abstract We are concerned with the stabilization of the wave equation with locally distributed mixed-type damping via arbitrary local viscoelastic and frictional effects. Here, one of the novelties is: the viscoelastic and frictional damping together effect only in a part of domain, not in entire domain, which is only assumed to meet the piecewise multiplier geometric condition that their summed interior and boundary measures can be arbitrarily small. Furthermore, there is no other additional restriction for the location of the viscoelastic-effect region. That is, it is dropped that the viscoelastic-effect region includes a part of the system boundary, which is the fundamental condition in almost all previous literature even if when two types of damping together cover the entire system domain. The other distinct novelty is: in this article we remove the fundamental condition that the derivative of the relaxation function is controlled by relaxation function itself, which is a necessity in the previous literature to obtain the optimal uniform decay rate. Under such weak conditions, we successfully establish a series of decay theorems, which generalize and extend essentially the previous related stability results for viscoelastic model regardless of local damping case, entire damping case and mixed-type damping case.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41880206","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

Singularity for a nonlinear degenerate hyperbolic-parabolic coupled system arising from nematic liquid crystals 由向列液晶产生的非线性退化双曲-抛物耦合系统的奇异性

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-11-19 DOI: 10.1515/anona-2022-0268

Yan-bo Hu

引用次数: 1

On a strongly damped semilinear wave equation with time-varying source and singular dissipation 具有时变震源和奇异耗散的强阻尼半线性波动方程

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-11-18 DOI: 10.1515/anona-2022-0267

Yi Yang, Z. Fang

引用次数: 6

A global compactness result with applications to a Hardy-Sobolev critical elliptic system involving coupled perturbation terms 一个全局紧性结果及其在含耦合扰动项的Hardy-Sobolev临界椭圆系统中的应用

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-11-16 DOI: 10.1515/anona-2022-0276

Lu Shun Wang, T. Yang, Xiao Long Yang

{"title":"A global compactness result with applications to a Hardy-Sobolev critical elliptic system involving coupled perturbation terms","authors":"Lu Shun Wang, T. Yang, Xiao Long Yang","doi":"10.1515/anona-2022-0276","DOIUrl":"https://doi.org/10.1515/anona-2022-0276","url":null,"abstract":"Abstract In this article, we study a Hardy-Sobolev critical elliptic system involving coupled perturbation terms: (0.1) − Δ u + V 1 ( x ) u = η 1 η 1 + η 2 ∣ u ∣ η 1 − 2 u ∣ v ∣ η 2 ∣ x ′ ∣ + α α + β Q ( x ) ∣ u ∣ α − 2 u ∣ v ∣ β , − Δ v + V 2 ( x ) v = η 2 η 1 + η 2 ∣ v ∣ η 2 − 2 v ∣ u ∣ η 1 ∣ x ′ ∣ + β α + β Q ( x ) ∣ v ∣ β − 2 v ∣ u ∣ α , left{begin{array}{c}-Delta u+{V}_{1}left(x)u=frac{{eta }_{1}}{{eta }_{1}+{eta }_{2}}frac{{| u| }^{{eta }_{1}-2}u{| v| }^{{eta }_{2}}}{| x^{prime} | }+frac{alpha }{alpha +beta }Qleft(x)| u{| }^{alpha -2}u| v{| }^{beta }, -Delta v+{V}_{2}left(x)v=frac{{eta }_{2}}{{eta }_{1}+{eta }_{2}}frac{{| v| }^{{eta }_{2}-2}v{| u| }^{{eta }_{1}}}{| x^{prime} | }+frac{beta }{alpha +beta }Qleft(x){| v| }^{beta -2}v{| u| }^{alpha },end{array}right. where n ≥ 3 nge 3 , 2 ≤ m < n 2le mlt n , x ≔ ( x ′ , x ″ ) ∈ R m × R n − m x:= left(x^{prime} ,{x}^{^{primeprime} })in {{mathbb{R}}}^{m}times {{mathbb{R}}}^{n-m} , η 1 , η 2 > 1 {eta }_{1},{eta }_{2}gt 1 , and η 1 + η 2 = 2 ( n − 1 ) n − 2 {eta }_{1}+{eta }_{2}=frac{2left(n-1)}{n-2} , α , β > 1 alpha ,beta gt 1 and α + β < 2 n n − 2 alpha +beta lt frac{2n}{n-2} , and V 1 ( x ) , V 2 ( x ) , Q ( x ) ∈ C ( R n ) {V}_{1}left(x),{V}_{2}left(x),Qleft(x)in Cleft({{mathbb{R}}}^{n}) . Observing that (0.1) is doubly coupled, we first develop two efficient tools (i.e., a refined Sobolev inequality and a variant of the “Vanishing” lemma). On the previous tools, we will establish a global compactness result (i.e., a complete description for the Palais-Smale sequences of the corresponding energy functional) and some existence result for (0.1) via variational method. Our strategy turns out to be very concise because we avoid the use of Levy concentration functions and truncation techniques.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2022-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49547812","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: 0

Touchdown solutions in general MEMS models 通用MEMS模型的触地解决方案

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-10-30 DOI: 10.1515/anona-2023-0102

R. Clemente, J. Marcos do Ó, Esteban da Silva, E. Shamarova

{"title":"Touchdown solutions in general MEMS models","authors":"R. Clemente, J. Marcos do Ó, Esteban da Silva, E. Shamarova","doi":"10.1515/anona-2023-0102","DOIUrl":"https://doi.org/10.1515/anona-2023-0102","url":null,"abstract":"Abstract We study general problems modeling electrostatic microelectromechanical systems devices (Pλ ) φ ( r , − u ′ ( r ) ) = λ ∫ 0 r f ( s ) g ( u ( s ) ) d s , r ∈ ( 0 , 1 ) , 0 < u ( r ) < 1 , r ∈ ( 0 , 1 ) , u ( 1 ) = 0 , left{begin{array}{ll}varphi (r,-u^{prime} left(r))=lambda underset{0}{overset{r}{displaystyle int }}frac{fleft(s)}{gleft(uleft(s))}{rm{d}}s,hspace{1.0em}& rin left(0,1), 0lt uleft(r)lt 1,hspace{1.0em}& rin left(0,1), uleft(1)=0,hspace{1.0em}end{array}right. where φ varphi , g g , and f f are some functions on [ 0 , 1 ] left[0,1] and λ > 0 lambda gt 0 is a parameter. We obtain results on the existence and regularity of a touchdown solution to ( P λ {P}_{lambda } ) and find upper and lower bounds on the respective pull-in voltage. In the particular case, when φ ( r , v ) = r α ∣ v ∣ β v varphi left(r,v)={r}^{alpha }{| v| }^{beta }v , i.e., when the associated differential equation involves the operator r − γ ( r α ∣ u ′ ∣ β u ′ ) ′ {r}^{-gamma }left({r}^{alpha }{| u^{prime} | }^{beta }u^{prime} )^{prime} , we obtain an exact asymptotic behavior of the touchdown solution in a neighborhood of the origin.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2022-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48254089","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: 1

Nonstationary Poiseuille flow of a non-Newtonian fluid with the shear rate-dependent viscosity 具有剪切速率相关粘度的非牛顿流体的非平稳Poiseuille流

IF 4.2 1区数学

Advances in Nonlinear Analysis Pub Date : 2022-10-26 DOI: 10.1515/anona-2022-0259

G. Panasenko, K. Pileckas

引用次数: 1