Pub Date : 2022-09-01DOI: 10.57262/die035-0910-641
Manoj Kumar, S Z Abbas
{"title":"Analysis of diffusive size-structured population model with stochastic perturbation","authors":"Manoj Kumar, S Z Abbas","doi":"10.57262/die035-0910-641","DOIUrl":"https://doi.org/10.57262/die035-0910-641","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48326930","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}
Pub Date : 2022-09-01DOI: 10.57262/die035-0910-611
Yan-bo Hu, Yating Qian
{"title":"An initial-boundary value problem for the two-dimensional rotating shallow water equations with axisymmetry","authors":"Yan-bo Hu, Yating Qian","doi":"10.57262/die035-0910-611","DOIUrl":"https://doi.org/10.57262/die035-0910-611","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44654329","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}
Pub Date : 2022-08-18DOI: 10.57262/die035-0910-559
L. Berezansky, Eric P. Braverman
. New explicit exponential stability conditions are presented for the non-autonomous scalar linear functional differential equation where h k ( t ) ≤ t , g ( t ) ≤ t , a k ( · ) and the kernel K ( · , · ) are oscillatory and, generally, discontinuous functions. The proofs are based on establish-ing boundedness of solutions and later using the exponential dichotomy for linear equations stating that either the homogeneous equation is exponentially stable or a non-homogeneous equation has an unbounded solution for some bounded right-hand side. Explicit tests are applied to models of population dynamics, such as controlled Hutchinson and Mackey-Glass equations. The results are illustrated with numerical examples, and connection to known tests is discussed.
． 给出了一类非自治标量线性泛函微分方程的显式指数稳定性条件，其中h k (t)≤t, g (t)≤t, a k(·)和核k(·，·)是振荡函数，一般为不连续函数。这些证明是基于建立解的有界性，然后使用线性方程的指数二分法来说明齐次方程是指数稳定的，或者非齐次方程在某个有界的右手边有无界解。显式测试应用于种群动态模型，如控制Hutchinson和Mackey-Glass方程。用数值算例说明了结果，并讨论了与已知试验的联系。
{"title":"On exponential stability of linear delay equations with oscillatory coefficients and kernels","authors":"L. Berezansky, Eric P. Braverman","doi":"10.57262/die035-0910-559","DOIUrl":"https://doi.org/10.57262/die035-0910-559","url":null,"abstract":". New explicit exponential stability conditions are presented for the non-autonomous scalar linear functional differential equation where h k ( t ) ≤ t , g ( t ) ≤ t , a k ( · ) and the kernel K ( · , · ) are oscillatory and, generally, discontinuous functions. The proofs are based on establish-ing boundedness of solutions and later using the exponential dichotomy for linear equations stating that either the homogeneous equation is exponentially stable or a non-homogeneous equation has an unbounded solution for some bounded right-hand side. Explicit tests are applied to models of population dynamics, such as controlled Hutchinson and Mackey-Glass equations. The results are illustrated with numerical examples, and connection to known tests is discussed.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44817473","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}
Pub Date : 2022-07-01DOI: 10.57262/die035-0708-437
Tiantian Liu, Hongjing Pan
{"title":"Global bifurcation curve for fourth-order MEMS/NEMS models","authors":"Tiantian Liu, Hongjing Pan","doi":"10.57262/die035-0708-437","DOIUrl":"https://doi.org/10.57262/die035-0708-437","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44349922","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}
Pub Date : 2022-07-01DOI: 10.57262/die035-0708-393
R. N. de Lima, Alânnio B. Nóbrega, M. Souto
{"title":"Existence of solutions for a class of integral equations","authors":"R. N. de Lima, Alânnio B. Nóbrega, M. Souto","doi":"10.57262/die035-0708-393","DOIUrl":"https://doi.org/10.57262/die035-0708-393","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47367242","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}
Pub Date : 2022-07-01DOI: 10.57262/die035-0708-451
Jing Chen, Yiqing Li
{"title":"Existence and concentration of ground state solutions for a critical Kirchhoff type equation in $mathbb R^2$","authors":"Jing Chen, Yiqing Li","doi":"10.57262/die035-0708-451","DOIUrl":"https://doi.org/10.57262/die035-0708-451","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48075888","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}
Pub Date : 2022-05-31DOI: 10.57262/die036-0304-247
R. Biswas, Sarika Goyal, K. Sreenadh
. In this article, we consider the following modified quasilinear critical Kirchhoff-Schr¨odinger problem involving Stein-Weiss type nonlinearity: where λ > 0 is a parameter, N = 0 < µ < N , 0 < 2 β + µ < N , 2 ≤ q < 2 p ∗ . Here p ∗ = NpN − p is the Sobolev critical exponent and p ∗ β,µ := p 2 (2 N − 2 β − µ ) N − 2 is the critical exponent with respect to the doubly weighted Hardy-Littlewood-Sobolev inequality (also called Stein- Weiss type inequality). Then by establishing a concentration-compactness argument for our problem, we show the existence of infinitely many nontrivial solutions to the equations with respect to the parameter λ by using Krasnoselskii’s genus theory, symmetric mountain pass theorem and Z 2 - symmetric version of mountain pass theorem for different range of q . We further show that these solutions belong to L ∞ ( R N ).
{"title":"Multiplicity results for $p$-Kirchhoff modified Schrödinger equations with Stein-Weiss type critical nonlinearity in $mathbb R^N$","authors":"R. Biswas, Sarika Goyal, K. Sreenadh","doi":"10.57262/die036-0304-247","DOIUrl":"https://doi.org/10.57262/die036-0304-247","url":null,"abstract":". In this article, we consider the following modified quasilinear critical Kirchhoff-Schr¨odinger problem involving Stein-Weiss type nonlinearity: where λ > 0 is a parameter, N = 0 < µ < N , 0 < 2 β + µ < N , 2 ≤ q < 2 p ∗ . Here p ∗ = NpN − p is the Sobolev critical exponent and p ∗ β,µ := p 2 (2 N − 2 β − µ ) N − 2 is the critical exponent with respect to the doubly weighted Hardy-Littlewood-Sobolev inequality (also called Stein- Weiss type inequality). Then by establishing a concentration-compactness argument for our problem, we show the existence of infinitely many nontrivial solutions to the equations with respect to the parameter λ by using Krasnoselskii’s genus theory, symmetric mountain pass theorem and Z 2 - symmetric version of mountain pass theorem for different range of q . We further show that these solutions belong to L ∞ ( R N ).","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44087334","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}
Pub Date : 2022-05-25DOI: 10.57262/die035-0910-581
A. Fernandez, J. Restrepo, D. Suragan
. Linear differential equations with variable coefficients and Prabhakar-type operators featuring Mittag-Leffler kernels are solved. In each case, the unique solution is constructed explicitly as a convergent infinite series involving compositions of Prabhakar fractional integrals. We also extend these results to Prabhakar operators with respect to functions. As an important illustrative example, we consider the case of constant coefficients, and give the solutions in a more closed form by using multivariate Mittag-Leffler functions.
{"title":"Prabhakar-type linear differential equations with variable coefficients","authors":"A. Fernandez, J. Restrepo, D. Suragan","doi":"10.57262/die035-0910-581","DOIUrl":"https://doi.org/10.57262/die035-0910-581","url":null,"abstract":". Linear differential equations with variable coefficients and Prabhakar-type operators featuring Mittag-Leffler kernels are solved. In each case, the unique solution is constructed explicitly as a convergent infinite series involving compositions of Prabhakar fractional integrals. We also extend these results to Prabhakar operators with respect to functions. As an important illustrative example, we consider the case of constant coefficients, and give the solutions in a more closed form by using multivariate Mittag-Leffler functions.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42625401","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}
Pub Date : 2022-05-01DOI: 10.57262/die035-0506-277
Michal Feckan, Jinrong Wang, Wenlin Zhang
{"title":"Existence of solutions for nonlinear elliptic equations modeling the steady flow of the antarctic circumpolar current","authors":"Michal Feckan, Jinrong Wang, Wenlin Zhang","doi":"10.57262/die035-0506-277","DOIUrl":"https://doi.org/10.57262/die035-0506-277","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43872931","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}
Pub Date : 2022-05-01DOI: 10.57262/die035-0506-339
S. Zagatti
{"title":"Non-convex one-dimensional functionals with superlinear growth","authors":"S. Zagatti","doi":"10.57262/die035-0506-339","DOIUrl":"https://doi.org/10.57262/die035-0506-339","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47565281","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}
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