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Differential Equations and Applications最新文献

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Weighted estimates and large time behavior of small amplitude solutions to the semilinear heat equation 半线性热方程小振幅解的加权估计和大时间特性
Differential Equations and Applications Pub Date : 2023-01-01 DOI: 10.7153/dea-2023-15-13
Ryunosuke Kusaba, Tohru Ozawa
{"title":"Weighted estimates and large time behavior of small amplitude solutions to the semilinear heat equation","authors":"Ryunosuke Kusaba, Tohru Ozawa","doi":"10.7153/dea-2023-15-13","DOIUrl":"https://doi.org/10.7153/dea-2023-15-13","url":null,"abstract":"We present a new method to obtain weighted $L^{1}$-estimates of global solutions to the Cauchy problem for the semilinear heat equation with a simple power of super-critical Fujita exponent. Our approach is based on direct and explicit computations of commutation relations between the heat semigroup and monomial weights in $mathbb{R}^{n}$, while it is independent of the standard parabolic arguments which rely on the comparison principle or some compactness arguments. We also give explicit asymptotic profiles with parabolic self-similarity of the global solutions.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135600136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the stability of systems of two linear first-order ordinary differential equations 两个一阶线性常微分方程系统的稳定性
Differential Equations and Applications Pub Date : 2023-01-01 DOI: 10.7153/dea-2023-15-15
G. A. Grigorian
{"title":"On the stability of systems of two linear first-order ordinary differential equations","authors":"G. A. Grigorian","doi":"10.7153/dea-2023-15-15","DOIUrl":"https://doi.org/10.7153/dea-2023-15-15","url":null,"abstract":"The Riccati equation method is used to establish some new stability criteria for systems of two linear first-order ordinary differential equations. It is shown that two of these criteria in the two dimensional case imply the Routh - Hurwitz's criterion.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"180 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unique solvability of second order nonlinear totally characteristic equations 二阶非线性全特征方程的唯一可解性
Differential Equations and Applications Pub Date : 2023-01-01 DOI: 10.7153/dea-2023-15-14
Michael E. Sta. Brigida, Jose Ernie C. Lope
{"title":"Unique solvability of second order nonlinear totally characteristic equations","authors":"Michael E. Sta. Brigida, Jose Ernie C. Lope","doi":"10.7153/dea-2023-15-14","DOIUrl":"https://doi.org/10.7153/dea-2023-15-14","url":null,"abstract":". We consider a second order singular nonlinear partial differential equation of the form ( t ∂ t ) 2 u = F ( t , x , u , ∂ x u , ∂ 2 x u , t ∂ t u , t ∂ t ∂ x u ) , where F is assumed to be continuous in t and holo-morphic with respect to the other variables. Under certain conditions, we prove that the equation has a unique solution that is continuous in t and holomorphic in x .","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"274 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135600133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Implicit Caputo fractional q-difference equations with non instantaneous impulses 非瞬时脉冲的隐式卡普托分数q差分方程
Differential Equations and Applications Pub Date : 2023-01-01 DOI: 10.7153/dea-2023-15-12
Saïd Abbas, Mouffak Benchohra, Alberto Cabada
{"title":"Implicit Caputo fractional q-difference equations with non instantaneous impulses","authors":"Saïd Abbas, Mouffak Benchohra, Alberto Cabada","doi":"10.7153/dea-2023-15-12","DOIUrl":"https://doi.org/10.7153/dea-2023-15-12","url":null,"abstract":". In the present article, we prove some existence results for a class of implicit Caputo fractional q -difference equations with non instantaneous impulses in Banach spaces. The used techniques rely on the concepts of measure of noncompactness and the use of suitable fi xed point theorems.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135600134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extremal solutions at infinity for symplectic systems on time scales II - Existence theory and limit properties 时间尺度上辛系统无穷远处的极值解II -存在论和极限性质
Differential Equations and Applications Pub Date : 2023-01-01 DOI: 10.7153/dea-2023-15-11
Iva Dřímalová
{"title":"Extremal solutions at infinity for symplectic systems on time scales II - Existence theory and limit properties","authors":"Iva Dřímalová","doi":"10.7153/dea-2023-15-11","DOIUrl":"https://doi.org/10.7153/dea-2023-15-11","url":null,"abstract":". In this paper we continue with our investigation of principal and antiprincipal solutions at in fi nity solutions of a dynamic symplectic system. The paper is a continuation of part I appeared in Differential Equations and Applications in 2022, where we have presenteded a theory of genera of conjoined bases for symplectic dynamic systems on time scales and its connections with principal solutions at in fi nity and antiprincipal solutions at in fi nity for these systems together with some basic properties of this new concept on time scales. Here we provide a characterization of all principal solutions of dynamic symplectic system at in fi nity in the given genus in terms of the initial conditions and a fi xed principal solution at in fi nity from this genus. Further, we provide a characterization of all antiprincipal solutions of dynamic symplectic system at in fi nity in the given genus in terms of the initial conditions and a fi xed principal solution at in fi nity from this genus. We also establish mutual limit properties of principal and antiprincipal solutions at in fi nity.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135600139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On persistence and invading species in ecological dynamics 论生态动力学中的持久性和入侵物种
Differential Equations and Applications Pub Date : 2021-01-01 DOI: 10.7153/DEA-2021-13-17
E. Sanchez-Palencia, J. Françoise
{"title":"On persistence and invading species in ecological dynamics","authors":"E. Sanchez-Palencia, J. Françoise","doi":"10.7153/DEA-2021-13-17","DOIUrl":"https://doi.org/10.7153/DEA-2021-13-17","url":null,"abstract":". The general problem of persistence of species, amounts to de fi ne interactions between them ensuring the survival of all the species initially present in the system. It appears that several relevant persistence schemes induce “forbidden sets” of zero measure for topological rea- sons. These peculiarities (without practical consequences) are nevertheless not consistent with certain mathematical de fi nitions of persistence, which are too much restrictive. We come back to de fi nitions of McGehee – Armstrong and their celebrated counter-example to the so-called “competitive exclusion principle”. We develop these concepts in relation with invasion properties of the species in a rather practical and computational framework. Several examples of communities exhibiting persistence without internal rest point (which necessarily exists according to strict persistence de fi nitions) are given, with explicit description of the attractors, forbidden sets and invasion properties. Mechanisms of contamination of these properties (based on elementary cartesian product and structural stability) are given, showing the widespreading nature of these schemes.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"21 1","pages":"297-320"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83292757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Coefficient inverse problem for the degenerate parabolic equation 退化抛物方程的系数反问题
Differential Equations and Applications Pub Date : 2021-01-01 DOI: 10.7153/DEA-2021-13-14
N. Huzyk
{"title":"Coefficient inverse problem for the degenerate parabolic equation","authors":"N. Huzyk","doi":"10.7153/DEA-2021-13-14","DOIUrl":"https://doi.org/10.7153/DEA-2021-13-14","url":null,"abstract":". The inverse problem for the degenerate parabolic equation is considered. The minor coef fi cient of the equation is a polynomial of the fi rst power with respect to the space variable with unknown time-dependent coef fi cients. The conditions of local in time existence and global uniqueness of the classical solution to this problem are established. The case of weak power degeneration is investigated.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"1 1","pages":"243-255"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86387591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Leggett-Williams fixed point theorem type for sums of operators and application in PDEs 算子和的Leggett-Williams不动点定理类型及其在偏微分方程中的应用
Differential Equations and Applications Pub Date : 2021-01-01 DOI: 10.7153/DEA-2021-13-18
S. Georgiev, K. Mebarki
{"title":"Leggett-Williams fixed point theorem type for sums of operators and application in PDEs","authors":"S. Georgiev, K. Mebarki","doi":"10.7153/DEA-2021-13-18","DOIUrl":"https://doi.org/10.7153/DEA-2021-13-18","url":null,"abstract":". In this paper we present an extension of the original version of Leggett-Williams fi xed point theorem for a k -set contraction perturbed by an expansive operator. Our approach is applied to prove the existence of non trivial positive solutions for initial value problems (IVPs for short) covering a class two-dimensional nonlinear wave equations.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"2012 1","pages":"321-344"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86399889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Existence and boundary behavior of solutions for boundary blow-up quasilinear elliptic problems with gradient terms 带梯度项的边界爆破拟线性椭圆问题解的存在性及边界行为
Differential Equations and Applications Pub Date : 2021-01-01 DOI: 10.7153/DEA-2021-13-16
Chunlian Liu
{"title":"Existence and boundary behavior of solutions for boundary blow-up quasilinear elliptic problems with gradient terms","authors":"Chunlian Liu","doi":"10.7153/DEA-2021-13-16","DOIUrl":"https://doi.org/10.7153/DEA-2021-13-16","url":null,"abstract":". In this paper, by sub-supersolution methods, Karamata regular variation theory and perturbation method, we study the existence, uniqueness and asymptotic behavior of solutions near the boundary to quasilinear elliptic problem where Ω is a bounded domain with smooth boundary in R N ( N (cid:2) 2 ) , 1 < m (cid:3) 2, 0 < q (cid:3) m / ( m − 1 ) . b ∈ C α ( Ω )( α ∈ ( 0 , 1 )) is positive in Ω , and may be vanishing on the boundary, and f ∈ C 1 [ 0 , + ∞ ) , f ( 0 ) = 0, is increase on ( 0 , + ∞ ) and normalized regularly varying at in fi nity with positive index p and p +( q − 1 )( m − 1 ) > 0.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"47 1","pages":"281-295"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85426643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Elzaki Substitution Method for Solving Nonlinear Partial Differential Equations with Mixed Partial Derivatives Using Adomain Polynomial 用域多项式求解混合偏导数非线性偏微分方程的Elzaki代换法
Differential Equations and Applications Pub Date : 2020-09-27 DOI: 10.12691/IJPDEA-8-1-2
Mousumi Datta, U. Habiba, Md. Babul Hossain
{"title":"Elzaki Substitution Method for Solving Nonlinear Partial Differential Equations with Mixed Partial Derivatives Using Adomain Polynomial","authors":"Mousumi Datta, U. Habiba, Md. Babul Hossain","doi":"10.12691/IJPDEA-8-1-2","DOIUrl":"https://doi.org/10.12691/IJPDEA-8-1-2","url":null,"abstract":"In this paper we apply a new method, named Elzaki Substitution Method to solve nonlinear homogeneous and nonhomogeneous partial differential equations with mixed partial derivatives, which is based on Elzaki Transform. The proposed method introduces also Adomain polynomials and the nonlinear terms can be handled by the use of this polynomials. The proposed method worked perfectly to find the exact solutions of partial equations with mixed partial derivatives without any need of linearization or discretization in comparison with other methods such as Method of Separation of Variables (MSV) and Variation Iteration Method (VIM). Some illustrative examples are given to demonstrate the applicability and efficiency of proposed method.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"14 1","pages":"6-12"},"PeriodicalIF":0.0,"publicationDate":"2020-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87128689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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