. The aim of the paper is to initiate a study of the oscillation of solutions of second order nonlinear differential equations with positive and negative nonlinear neutral terms. The results are illustrated by some examples.
． 本文的目的是研究二阶非线性微分方程正、负非线性中立项解的振动性。算例说明了计算结果。
{"title":"Oscillatory behavior of second order nonlinear delay differential equations with positive and negative neutral terms","authors":"S. Grace, J. Graef, I. Jadlovská","doi":"10.7153/dea-2020-12-13","DOIUrl":"https://doi.org/10.7153/dea-2020-12-13","url":null,"abstract":". The aim of the paper is to initiate a study of the oscillation of solutions of second order nonlinear differential equations with positive and negative nonlinear neutral terms. The results are illustrated by some examples.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130200","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}
This article deals with some questions of existence and uniqueness of random solutions for some coupled systems of random Hilfer and Hilfer–Hadamard fractional differential equations with finite delay. We use some generalizations of classical random fixed point theorems on generalized Banach spaces.
{"title":"Coupled Hilfer and Hadamard random fractional differential systems with finite delay in generalized Banach spaces","authors":"S. Abbas, N. Al Arifi, M. Benchohra, J. Henderson","doi":"10.7153/dea-2020-12-22","DOIUrl":"https://doi.org/10.7153/dea-2020-12-22","url":null,"abstract":"This article deals with some questions of existence and uniqueness of random solutions for some coupled systems of random Hilfer and Hilfer–Hadamard fractional differential equations with finite delay. We use some generalizations of classical random fixed point theorems on generalized Banach spaces.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130982","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}
. In this paper, the homogenization problem for the Klein-Gordon type equation is stud- ied in the almost periodic setting. The propagation speed and the potential are spatial and time dependent almost periodically varying functions. One convergence theorem is proved and we derive the macroscopic homogenized model veri fi ed by the mean wave function.
{"title":"Almost periodic homogenization of the Klein-Gordon type equation","authors":"Lazarus Signing","doi":"10.7153/dea-2020-12-10","DOIUrl":"https://doi.org/10.7153/dea-2020-12-10","url":null,"abstract":". In this paper, the homogenization problem for the Klein-Gordon type equation is stud- ied in the almost periodic setting. The propagation speed and the potential are spatial and time dependent almost periodically varying functions. One convergence theorem is proved and we derive the macroscopic homogenized model veri fi ed by the mean wave function.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"37 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130145","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}
. This paper concerns the existence and stability results for ψ -type complex-order im- plicit differential equations with boundary conditions. The results are based on the Banach contraction mapping principle. An example is presented to illustrate the main results.
{"title":"Existence theory and stability results for ψ-type complex-order implicit differential equations","authors":"D. Vivek, S. Ntouyas, K. Kanagarajan, J. Prasanth","doi":"10.7153/dea-2020-12-14","DOIUrl":"https://doi.org/10.7153/dea-2020-12-14","url":null,"abstract":". This paper concerns the existence and stability results for ψ -type complex-order im- plicit differential equations with boundary conditions. The results are based on the Banach contraction mapping principle. An example is presented to illustrate the main results.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130280","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}
In Theorem 3 of [2] I included an extension to the Ascoli theorem. While the statement of the theorem and its later use were correct, the proof has a slight error which I noticed while in the process of writing a sequel. Also a few comments about the complete continuity of an operator are provided as well as well as an additional reference. Mathematics subject classification (2010): 34B18, 34A34, 34A36, 34A60, 34B15, 47H10.
{"title":"Corrigendum to: Positive solutions for a fourth order differential inclusion with boundary values, published in Differential Equations and Applications Vol. 8 No. 1 (2016), 21-31, by John S. Spraker","authors":"John S. Spraker","doi":"10.7153/dea-2020-12-07","DOIUrl":"https://doi.org/10.7153/dea-2020-12-07","url":null,"abstract":"In Theorem 3 of [2] I included an extension to the Ascoli theorem. While the statement of the theorem and its later use were correct, the proof has a slight error which I noticed while in the process of writing a sequel. Also a few comments about the complete continuity of an operator are provided as well as well as an additional reference. Mathematics subject classification (2010): 34B18, 34A34, 34A36, 34A60, 34B15, 47H10.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130098","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}
. In this paper we are going to study existence and multiplicity of solutions of a system involving fractional Kirchhoff-type and critical growth of form where s ∈ ( 0 , 1 ) , n > 2 s , Ω ⊂ R n is a bounded and open set, 2 ∗ s = 2 n / ( n − 2 s ) denotes the fractional critical Sobolev exponent, the functions M 1 , M 2 , f and g are continuous functions, ( − Δ ) s is the fractional laplacian operator, || . || X is a norm in the fractional Hilbert Sobolev space X ( Ω ) , F ( x , v ( x )) = v x , G x , ( x )) g ( τ ) d τ , r 1 and r 2 are positive constants, λ and γ are real parameters. For this problem we prove the existence of in fi nitely many solutions, via a suitable truncation argument and exploring the genus theory introduced by Krasnoselskii. Also we show that these solutions are suf fi ciently regular and solve the problem pointwise.
． 在本文中,我们要学习系统的存在性和多重性的解决方案涉及部分Kirchhoff-type和形式的关键增长年代∈(0,1),n > 2 s,Ω⊂R n是一个有界和开集,2∗s = 2 n / (n−2 s)表示部分关键水列夫指数函数米1米2,f和g是连续函数,(−Δ)年代分数拉普拉斯算符,| |。|| X是分数阶Hilbert Sobolev空间X (Ω)中的范数，F (X, v (X)) = vx, gx， (X)) G (τ) d τ， r1和r2是正常数，λ和γ是实参数。对于这个问题，我们通过适当的截断论证和Krasnoselskii引入的属理论，证明了有限多个解的存在性。我们还证明了这些解是充分正则的，并能逐点求解问题。
{"title":"Multiple solutions of systems involving fractional Kirchhoff-type equations with critical growth","authors":"A. Costa, B. Maia","doi":"10.7153/dea-2020-12-11","DOIUrl":"https://doi.org/10.7153/dea-2020-12-11","url":null,"abstract":". In this paper we are going to study existence and multiplicity of solutions of a system involving fractional Kirchhoff-type and critical growth of form where s ∈ ( 0 , 1 ) , n > 2 s , Ω ⊂ R n is a bounded and open set, 2 ∗ s = 2 n / ( n − 2 s ) denotes the fractional critical Sobolev exponent, the functions M 1 , M 2 , f and g are continuous functions, ( − Δ ) s is the fractional laplacian operator, || . || X is a norm in the fractional Hilbert Sobolev space X ( Ω ) , F ( x , v ( x )) = v x , G x , ( x )) g ( τ ) d τ , r 1 and r 2 are positive constants, λ and γ are real parameters. For this problem we prove the existence of in fi nitely many solutions, via a suitable truncation argument and exploring the genus theory introduced by Krasnoselskii. Also we show that these solutions are suf fi ciently regular and solve the problem pointwise.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130187","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}
. In this paper, a system of quasilinear elliptic equations is investigated, which involves multiple critical Hardy-Sobolev exponents and symmetric multi-polar potentials. By employing the variational methods and analytic techniques, the relevant best constants are studied and the existence of ( Z k × SO ( N − 2 )) 2 -invariant solutions to the system is established.
． 研究了一类包含多个临界Hardy-Sobolev指数和对称多极势的拟线性椭圆方程。利用变分方法和解析技术，研究了系统的最佳常数，建立了系统的(zk × SO (N−2))2不变解的存在性。
{"title":"A variational method for solving quasilinear elliptic systems involving symmetric multi-polar potentials","authors":"A. Rashidi, M. Shekarbaigi","doi":"10.7153/dea-2020-12-23","DOIUrl":"https://doi.org/10.7153/dea-2020-12-23","url":null,"abstract":". In this paper, a system of quasilinear elliptic equations is investigated, which involves multiple critical Hardy-Sobolev exponents and symmetric multi-polar potentials. By employing the variational methods and analytic techniques, the relevant best constants are studied and the existence of ( Z k × SO ( N − 2 )) 2 -invariant solutions to the system is established.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"52 Suppl 1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130560","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}
. We consider the initial value problem associated to a system consisting modi fi ed Korteweg-de Vries type equations and using only bilinear estimates of the type (cid:2) J γ F 1 b 1 J F 2 b 2 (cid:2) L 2 x L 2 t , where J is the Bessel potential and F jb j , j = 1 , 2 are multiplication operators, we prove the local well-posedness results for given data in low regularity Sobolev spaces H s ( R ) × H k ( R ) for α (cid:3) = 0 , 1. In this work we improve the previous result in [6], extending the LWP region from | s − k | < 1 / 2 to | s − k | < 1. This result is sharp in the region of the LWP with s (cid:2) 0 and k (cid:2) 0, in the sense of the trilinear estimates fails to hold.
． 我们认为相关的初值问题系统组成莫迪fi ed Korteweg-de弗里斯类型方程和只使用双线性估计的类型(cid: 2) Jγ1 b J F 2 b 2 (cid: 2) L 2 x L 2 t,其中J是贝塞尔潜力和F jb J, J = 1, 2是乘法运算符,我们证明了本地结果适定性问题给定数据在低规律性索伯列夫空间H s (R)×H k (R)α(cid: 3) = 0, 1。在这项工作中，我们改进了先前在[6]中的结果，将LWP区域从| s−k | < 1 / 2扩展到| s−k | < 1。这个结果在s (cid:2) 0和k (cid:2) 0的LWP区域是明显的，在三线性估计不成立的意义上。
{"title":"A remark on the local well-posedness for a coupled system of mKdV type equations in H^s × H^k","authors":"X. Carvajal","doi":"10.7153/dea-2020-12-27","DOIUrl":"https://doi.org/10.7153/dea-2020-12-27","url":null,"abstract":". We consider the initial value problem associated to a system consisting modi fi ed Korteweg-de Vries type equations and using only bilinear estimates of the type (cid:2) J γ F 1 b 1 J F 2 b 2 (cid:2) L 2 x L 2 t , where J is the Bessel potential and F jb j , j = 1 , 2 are multiplication operators, we prove the local well-posedness results for given data in low regularity Sobolev spaces H s ( R ) × H k ( R ) for α (cid:3) = 0 , 1. In this work we improve the previous result in [6], extending the LWP region from | s − k | < 1 / 2 to | s − k | < 1. This result is sharp in the region of the LWP with s (cid:2) 0 and k (cid:2) 0, in the sense of the trilinear estimates fails to hold.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130622","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}
. We investigate fractional order delay and neutral differential equations. By using Ba- nach fi xed point theorem we establish existence and uniqueness of the solutions for fractional order functional differential equations involving Hilfer fractional derivative in the weighted spaces.
{"title":"Existence and uniqueness for fractional order functional differential equations with Hilfer derivative","authors":"F. Karakoç","doi":"10.7153/dea-2020-12-21","DOIUrl":"https://doi.org/10.7153/dea-2020-12-21","url":null,"abstract":". We investigate fractional order delay and neutral differential equations. By using Ba- nach fi xed point theorem we establish existence and uniqueness of the solutions for fractional order functional differential equations involving Hilfer fractional derivative in the weighted spaces.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130965","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}
Gleiciane S. Aragão, F. Bezerra, C. O. P. D. Silva
In this paper we show the lower semicontinuity of the global attractors of autonomous thermoelastic plate systems with Neumann boundary conditions when some reaction terms are concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary as a parameter $varepsilon$ goes to zero.
{"title":"Dynamics of thermoelastic plate system with terms concentrated in the boundary","authors":"Gleiciane S. Aragão, F. Bezerra, C. O. P. D. Silva","doi":"10.7153/DEA-2019-11-18","DOIUrl":"https://doi.org/10.7153/DEA-2019-11-18","url":null,"abstract":"In this paper we show the lower semicontinuity of the global attractors of autonomous thermoelastic plate systems with Neumann boundary conditions when some reaction terms are concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary as a parameter $varepsilon$ goes to zero.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43521483","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}
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