Pub Date : 2023-01-01DOI: 10.57262/ade028-1112-889
Yining Chen, Yufeng Wang, Jianshe Yu, Bo Zheng, Zhongcai Zhu
{"title":"Global dynamics of a mosquito population suppression model with seasonal switching","authors":"Yining Chen, Yufeng Wang, Jianshe Yu, Bo Zheng, Zhongcai Zhu","doi":"10.57262/ade028-1112-889","DOIUrl":"https://doi.org/10.57262/ade028-1112-889","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71111719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.57262/ade028-1112-921
M. Winkler
{"title":"Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing","authors":"M. Winkler","doi":"10.57262/ade028-1112-921","DOIUrl":"https://doi.org/10.57262/ade028-1112-921","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71111771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.57262/ade028-1112-953
Houria Chellaoua, Y. Boukhatem, B. Feng
{"title":"Well-posedness and stability for an abstract evolution equation with history memory and time delay in Hilbert space","authors":"Houria Chellaoua, Y. Boukhatem, B. Feng","doi":"10.57262/ade028-1112-953","DOIUrl":"https://doi.org/10.57262/ade028-1112-953","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71111782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.57262/ade028-0102-143
M. Jleli, M. Ragusa, B. Samet
{"title":"Nonlinear Liouville-type theorems for generalized Baouendi-Grushin operator on Riemannian manifolds","authors":"M. Jleli, M. Ragusa, B. Samet","doi":"10.57262/ade028-0102-143","DOIUrl":"https://doi.org/10.57262/ade028-0102-143","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44589456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Qualitative properties of singular solutions of Choquard equations","authors":"Huyuan Chen, F. Zhou","doi":"10.57262/ade028-0102-35","DOIUrl":"https://doi.org/10.57262/ade028-0102-35","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46988493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-30DOI: 10.57262/ade028-0708-685
E. Tavares, M. A. J. Silva, V. Narciso, A. Vicente
This work is concerned with new results on long-time dynamics of a class of hyperbolic evolution equations related to extensible beams with three distinguished nonlocal nonlinear damping terms. In the first possibly degenerate case, the results feature the existence of a family of compact global attractors and a thickness estimate for their Kolmogorov's $varepsilon$-entropy. Then, in the non-degenerate context, the structure of the helpful nonlocal damping leads to the existence of finite-dimensional compact global and exponential attractors. Lastly, in a degenerate and critical framework, it is proved the existence of a bounded closed global attractor but not compact. To the proofs, we provide several new technical results by means of refined estimates that open up perspectives for a new branch of nonlinearly damped problems.
{"title":"Dynamics of a class of extensible beams with degenerate and non-degenerate nonlocal damping","authors":"E. Tavares, M. A. J. Silva, V. Narciso, A. Vicente","doi":"10.57262/ade028-0708-685","DOIUrl":"https://doi.org/10.57262/ade028-0708-685","url":null,"abstract":"This work is concerned with new results on long-time dynamics of a class of hyperbolic evolution equations related to extensible beams with three distinguished nonlocal nonlinear damping terms. In the first possibly degenerate case, the results feature the existence of a family of compact global attractors and a thickness estimate for their Kolmogorov's $varepsilon$-entropy. Then, in the non-degenerate context, the structure of the helpful nonlocal damping leads to the existence of finite-dimensional compact global and exponential attractors. Lastly, in a degenerate and critical framework, it is proved the existence of a bounded closed global attractor but not compact. To the proofs, we provide several new technical results by means of refined estimates that open up perspectives for a new branch of nonlinearly damped problems.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45051066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-10DOI: 10.57262/ade028-0304-311
Pascal B'egout, Jes'us Ildefonso D'iaz
This paper completes some previous studies by several authors on the finite time extinction for nonlinear Schr{"o}dinger equation when the nonlinear damping term corresponds to the limit cases of some ``saturating non-Kerr law'' $F(|u|^2)u=frac{a}{varepsilon+(|u|^2)^alpha}u,$ with $ainmathbb{C},$ $varepsilongeqslant0,$ $2alpha=(1-m)$ and $min[0,1).$ Here we consider the sublinear case $00 text{ and } 2sqrt{m}mathrm{Im}(z)=(1-m)mathrm{Re}(z)big}.$ Among other things, we know that this damping coefficient is critical, for instance, in order to obtain the monotonicity of the associated operator (see the paper by Liskevich and Perel'muter [16] and the more recent study by Cialdea and Maz'ya [14]). The finite time extinction of solutions is proved by a suitable energy method after obtaining appropiate a priori estimates. Most of the results apply to non-necessarily bounded spatial domains.
{"title":"Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity","authors":"Pascal B'egout, Jes'us Ildefonso D'iaz","doi":"10.57262/ade028-0304-311","DOIUrl":"https://doi.org/10.57262/ade028-0304-311","url":null,"abstract":"This paper completes some previous studies by several authors on the finite time extinction for nonlinear Schr{\"o}dinger equation when the nonlinear damping term corresponds to the limit cases of some ``saturating non-Kerr law'' $F(|u|^2)u=frac{a}{varepsilon+(|u|^2)^alpha}u,$ with $ainmathbb{C},$ $varepsilongeqslant0,$ $2alpha=(1-m)$ and $min[0,1).$ Here we consider the sublinear case $0<m<1$ with a critical damped coefficient: $ainmathbb{C}$ is assumed to be in the set $D(m)=big{zinmathbb{C}; ; mathrm{Im}(z)>0 text{ and } 2sqrt{m}mathrm{Im}(z)=(1-m)mathrm{Re}(z)big}.$ Among other things, we know that this damping coefficient is critical, for instance, in order to obtain the monotonicity of the associated operator (see the paper by Liskevich and Perel'muter [16] and the more recent study by Cialdea and Maz'ya [14]). The finite time extinction of solutions is proved by a suitable energy method after obtaining appropiate a priori estimates. Most of the results apply to non-necessarily bounded spatial domains.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47570799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-01DOI: 10.57262/ade027-0910-611
Shengda Zeng, Vicentiu D. Rădulescu, Patrick Winkert
. This paper is devoted to the study of a quasilinear elliptic inclusion problem driven by a double phase differential operator with variable exponents, an obstacle effect and a multival-ued reaction term with gradient dependence. By using an existence result for mixed variational inequalities with multivalued pseudomonotone operators and the theory of nonsmooth analysis, we examine the nonemptiness, boundedness and closedness of the solution set to the problem under consideration. In the second part of the paper we present some convergence analysis for approximated problems. To be more precise, when the obstacle function is approximated by a suitable sequence, applying a generalized penalty technique, we introduce a family of perturbed problems without constraints associated to our problem and prove that the solution set of the original problem can be approached by the solution sets of the perturbed problems in the sense of Kuratowski.
{"title":"Double phase obstacle problems with variable exponent","authors":"Shengda Zeng, Vicentiu D. Rădulescu, Patrick Winkert","doi":"10.57262/ade027-0910-611","DOIUrl":"https://doi.org/10.57262/ade027-0910-611","url":null,"abstract":". This paper is devoted to the study of a quasilinear elliptic inclusion problem driven by a double phase differential operator with variable exponents, an obstacle effect and a multival-ued reaction term with gradient dependence. By using an existence result for mixed variational inequalities with multivalued pseudomonotone operators and the theory of nonsmooth analysis, we examine the nonemptiness, boundedness and closedness of the solution set to the problem under consideration. In the second part of the paper we present some convergence analysis for approximated problems. To be more precise, when the obstacle function is approximated by a suitable sequence, applying a generalized penalty technique, we introduce a family of perturbed problems without constraints associated to our problem and prove that the solution set of the original problem can be approached by the solution sets of the perturbed problems in the sense of Kuratowski.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44295310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-01DOI: 10.57262/ade027-0910-543
Yingying Xiao, Chuanxi Zhu
{"title":"On Chern-Simons-Schrödinger systems involving steep potential well and concave-convex nonlinearities","authors":"Yingying Xiao, Chuanxi Zhu","doi":"10.57262/ade027-0910-543","DOIUrl":"https://doi.org/10.57262/ade027-0910-543","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48470568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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