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Nontrivial solutions of quasilinear Choquard equation involving the $p$-Laplacian operator and critical nonlinearities 包含$p$-Laplacian算子和临界非线性的拟线性Choquard方程的非平凡解
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2022-05-01 DOI: 10.57262/die035-0506-359
Shuaishuai Liang, Yueqiang Song
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引用次数: 2
Symmetry of intrinsically singular solutions of double phase problems 双相问题固有奇异解的对称性
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2022-04-19 DOI: 10.57262/die036-0304-229
Stefano Biagi, F. Esposito, E. Vecchi
{"title":"Symmetry of intrinsically singular solutions of double phase problems","authors":"Stefano Biagi, F. Esposito, E. Vecchi","doi":"10.57262/die036-0304-229","DOIUrl":"https://doi.org/10.57262/die036-0304-229","url":null,"abstract":"where Ω ⊂ R , 1 < p < q < N and a(·) ≥ 0. This class of functionals naturally appear in homogenization theory and in the study of strongly anisotropic materials (see, e.g., [39]), and falls into the framework of the so called functionals with non-standard growth introduced by Marcellini [27, 28]. The literature concerning functionals like (1.1) is pretty vast and concerns as a main topic the regularity of minimizers, see e.g. [2, 11, 12, 23] and the references therein.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41410774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Local boundedness for forward-backward parabolic De Giorgi classes without assuming higher regularity 不假设较高正则性的正反抛物型De Giorgi类的局部有界性
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2022-03-01 DOI: 10.57262/die035-0304-151
F. Paronetto
{"title":"Local boundedness for forward-backward parabolic De Giorgi classes without assuming higher regularity","authors":"F. Paronetto","doi":"10.57262/die035-0304-151","DOIUrl":"https://doi.org/10.57262/die035-0304-151","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41614001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Ground state and least positive energy solutions of elliptic problems involving mixed fractional $p$-Laplacians 混合分数阶拉普拉斯椭圆问题的基态解和最小正能量解
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2022-03-01 DOI: 10.57262/die035-0304-173
H. Hajaiej, K. Perera
{"title":"Ground state and least positive energy solutions of elliptic problems involving mixed fractional $p$-Laplacians","authors":"H. Hajaiej, K. Perera","doi":"10.57262/die035-0304-173","DOIUrl":"https://doi.org/10.57262/die035-0304-173","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47068861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Positive eigenfunctions of a class of fractional Schrödinger operator with a potential well 一类具有势阱的分数阶Schrödinger算子的正本征函数
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2022-01-01 DOI: 10.57262/die035-0102-123
Guangze Gu, Zhipeng Yang
{"title":"Positive eigenfunctions of a class of fractional Schrödinger operator with a potential well","authors":"Guangze Gu, Zhipeng Yang","doi":"10.57262/die035-0102-123","DOIUrl":"https://doi.org/10.57262/die035-0102-123","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49041241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Positive solutions of fractional Schrödinger-Poisson systems involving critical nonlinearities with potential 含势临界非线性的分数阶Schrödinger-Poisson系统的正解
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2022-01-01 DOI: 10.57262/die035-0102-1
H. Fan, Zhaosheng Feng, Xingjie Yan
{"title":"Positive solutions of fractional Schrödinger-Poisson systems involving critical nonlinearities with potential","authors":"H. Fan, Zhaosheng Feng, Xingjie Yan","doi":"10.57262/die035-0102-1","DOIUrl":"https://doi.org/10.57262/die035-0102-1","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47283086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Asymptotic behavior of blowing-up radial solutions for quasilinear elliptic systems arising in the study of viscous, heat conducting fluids 粘性导热流体研究中出现的拟线性椭圆系统爆破径向解的渐近行为
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-12-28 DOI: 10.57262/die035-0910-511
A. Bachir, J. Giacomoni, G. Warnault
{"title":"Asymptotic behavior of blowing-up radial solutions for quasilinear elliptic systems arising in the study of viscous, heat conducting fluids","authors":"A. Bachir, J. Giacomoni, G. Warnault","doi":"10.57262/die035-0910-511","DOIUrl":"https://doi.org/10.57262/die035-0910-511","url":null,"abstract":"In this paper, we deal with the following quasilinear elliptic system involving gradient terms in the form: { ∆pu = v |∇u| in Ω ∆pv = v β |∇u| in Ω, where Ω ⊂ R (N ≥ 2) is either equal to R or equal to a ball BR centered at the origin and having radius R > 0, 1 < p < ∞, m, q > 0, α ≥ 0, 0 ≤ β ≤ m and δ := (p− 1− α)(p− 1− β)− qm 6= 0. Our aim is to establish the asymptotics of the blowing-up radial solutions to the above system. Precisely, we provide the accurate asymptotic behavior at the boundary for such blowing-up radial solutions. For that,we prove a strong maximal principle for the problem of independent interest and study an auxiliary asymptotically autonomous system in R.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43644838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Boundary control and homogenization: Optimal climatization through smart double skin boundaries 边界控制和均质化:通过智能双皮肤边界的最佳气候
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-12-23 DOI: 10.57262/die035-0304-191
J. I. D'iaz, A. V. Podolskiy, T. Shaposhnikova
{"title":"Boundary control and homogenization: Optimal climatization through smart double skin boundaries","authors":"J. I. D'iaz, A. V. Podolskiy, T. Shaposhnikova","doi":"10.57262/die035-0304-191","DOIUrl":"https://doi.org/10.57262/die035-0304-191","url":null,"abstract":"We consider the homogenization of an optimal control problem in which the control v is placed on a part Γ0 of the boundary and the spatial domain contains a thin layer of “small particles”, very close to the controlling boundary, and a Robin boundary condition is assumed on the boundary of those “small particles”. This problem can be associated with the climatization modeling of Bioclimatic Double Skin Façades which was developed in modern architecture as a tool for energy optimization. We assume that the size of the particles and the parameters involved in the Robin boundary condition are critical (and so they justify the occurrence of some “strange terms” in the homogenized problem). The cost functional is given by a weighted balance of the distance (in a H-type metric) to a prescribed target internal temperature uT and the proper cost of the control v (given by its L(Γ0) norm). We prove the (weak) convergence of states uε and of the controls vε to some functions, u0 and v0, respectively, which are completely identified: u0 satisfies an artificial boundary condition on Γ0 and v0 is the optimal control associated to a limit cost functional J0 in which the “boundary strange term” on Γ0 arises. This information on the limit problem makes much more manageable the study of the optimal climatization of such double skin structures.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44368013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Anisotropic and isotropic persistent singularities of solutions of the fast diffusion equation 快速扩散方程解的各向异性和各向同性持久奇点
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-11-15 DOI: 10.57262/die035-1112-729
M. Fila, Petra Mackov'a, J. Takahashi, E. Yanagida
{"title":"Anisotropic and isotropic persistent singularities of solutions of the fast diffusion equation","authors":"M. Fila, Petra Mackov'a, J. Takahashi, E. Yanagida","doi":"10.57262/die035-1112-729","DOIUrl":"https://doi.org/10.57262/die035-1112-729","url":null,"abstract":"Abstract. The aim of this paper is to study a class of positive solutions of the fast diffusion equation with specific persistent singular behavior. First, we construct new types of solutions with anisotropic singularities. Depending on parameters, either these solutions solve the original equation in the distributional sense, or they are not locally integrable in space-time. We show that the latter also holds for solutions with snaking singularities, whose existence has been proved recently by M. Fila, J.R. King, J. Takahashi, and E. Yanagida. Moreover, we establish that in the distributional sense, isotropic solutions whose existence was proved by M. Fila, J. Takahashi, and E. Yanagida in 2019, actually solve the corresponding problem with a moving Dirac source term. Last, we discuss the existence of solutions with anisotropic singularities in a critical case.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47733555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Local uniform convergence and eventual positivity of solutions to biharmonic heat equations 双调和热方程解的局部一致收敛性和最终正性
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-11-04 DOI: 10.57262/die036-0910-727
D. Daners, Jochen Gluck, J. Mui
{"title":"Local uniform convergence and eventual positivity of solutions to biharmonic heat equations","authors":"D. Daners, Jochen Gluck, J. Mui","doi":"10.57262/die036-0910-727","DOIUrl":"https://doi.org/10.57262/die036-0910-727","url":null,"abstract":"We study the evolution equation associated with the biharmonic operator on infinite cylinders with bounded smooth cross-section subject to Dirichlet boundary conditions. The focus is on the asymptotic behaviour and positivity properties of the solutions for large times. In particular, we derive the local eventual positivity of solutions. We furthermore prove the local eventual positivity of solutions to the biharmonic heat equation and its generalisations on Euclidean space. The main tools in our analysis are the Fourier transform and spectral methods.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43501794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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