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Periodic solutions for nonlinear fractional differential systems 非线性分数阶微分系统的周期解
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-21
S. Abbas, M. Benchohra, S. Bouriah, J. Nieto
{"title":"Periodic solutions for nonlinear fractional differential systems","authors":"S. Abbas, M. Benchohra, S. Bouriah, J. Nieto","doi":"10.7153/DEA-2018-10-21","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-21","url":null,"abstract":"In this paper, we establish some existence and uniqueness results for periodic solutions for a class of fractional differential equations with the Caputo fractional derivative. The arguments are based upon the Banach contraction principle, and Schaefer’s fixed point theorem.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"52 1","pages":"299-316"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74869333","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: 3
Factorization techniques for the nonlinear model of quasi-stationary processes in crystalline semiconductors 晶体半导体中准平稳过程非线性模型的因子分解技术
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-24
B. Juárez-Campos, E. Kaikina, P. Naumkin, H. R. Paredes
{"title":"Factorization techniques for the nonlinear model of quasi-stationary processes in crystalline semiconductors","authors":"B. Juárez-Campos, E. Kaikina, P. Naumkin, H. R. Paredes","doi":"10.7153/DEA-2018-10-24","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-24","url":null,"abstract":"We consider the question of global existence and asymptotics of small solutions of a certain pseudoparabolic equation in one dimension . This model is motivated by the wave equation for media with a strong spatial dispersion, which appear in the nonlinear theory of the quasi-stationary processes in the electric media. We develop the factorization technique to study the large time asymptotics of solutions.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"52 1","pages":"341-367"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90672289","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
Box-counting dimension of oscillatory solutions to the Emden-Fowler equation Emden-Fowler方程振荡解的盒计数维数
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-17
Takanao Kanemitsu, Satoshi Tanaka
{"title":"Box-counting dimension of oscillatory solutions to the Emden-Fowler equation","authors":"Takanao Kanemitsu, Satoshi Tanaka","doi":"10.7153/DEA-2018-10-17","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-17","url":null,"abstract":"The box-counting dimension of graphs of oscillatory solutions to the Emden-Fowler equation is studied. The half-linear equation is also considered. Mathematics subject classification (2010): 34C10, 28A80.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"252 1","pages":"239-250"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77643463","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
Lower bounds for the first zero for nonlinear second order differential equations 二阶非线性微分方程第一个零的下界
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/dea-2018-10-13
D. Biles
{"title":"Lower bounds for the first zero for nonlinear second order differential equations","authors":"D. Biles","doi":"10.7153/dea-2018-10-13","DOIUrl":"https://doi.org/10.7153/dea-2018-10-13","url":null,"abstract":"We consider establishing lower bounds for the first zero of the solution of the nonlinear second order initial value problem (p(x)y′(x))′ + f (x,y(x)) = 0, x 0 y(0) = a > 0, y′(0) = 0. Using the linear case as a starting point, we prove several of these theorems, comparing them by considering several examples. Mathematics subject classification (2010): 34C10, 34A34, 34A36.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"15 3 1","pages":"209-218"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75796627","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
Existence and multiplicity results for the fractional p-Laplacian equation with Hardy-Sobolev exponents 具有Hardy-Sobolev指数的分数阶p- laplace方程的存在性和多重性结果
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/dea-2018-10-06
Gai ia Ning, Zhiyong Wang, Jihui Zhang
{"title":"Existence and multiplicity results for the fractional p-Laplacian equation with Hardy-Sobolev exponents","authors":"Gai ia Ning, Zhiyong Wang, Jihui Zhang","doi":"10.7153/dea-2018-10-06","DOIUrl":"https://doi.org/10.7153/dea-2018-10-06","url":null,"abstract":"In this paper, we investigate the following fractional p -Laplacian problem ⎨⎩ (−Δ)pu = λ |u|p−2u+ |u| ps,α−2u |x|α in Ω, u = 0 on ∂Ω, where Ω is a bounded domain containing the origin in RN with Lipschitz boundary, p ∈ (1,∞) , s ∈ (0,1) , 0 α < ps < N and p∗s,α = (N −α)p/(N − ps) is the fractional Hardy-Sobolev exponent. We prove the existence, multiplicity and bifurcation results for the above problem. Our results extend some results in the literature for the fractional p -Laplacian problem involving critical Sobolev exponent and the p -Laplacian problem involving Hardy-Sobolev exponents.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"26 1","pages":"87-114"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78741948","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 sign-changing solutions for resonant (p,q)-Laplace equations 共振(p,q)-拉普拉斯方程的变符号解
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/dea-2018-10-12
V. Bobkov, Mieko Tanaka
{"title":"On sign-changing solutions for resonant (p,q)-Laplace equations","authors":"V. Bobkov, Mieko Tanaka","doi":"10.7153/dea-2018-10-12","DOIUrl":"https://doi.org/10.7153/dea-2018-10-12","url":null,"abstract":". We provide two existence results for sign-changing solutions to the Dirichlet problem for the family of equations − ∆ p u − ∆ q u = α | u | p − 2 u + β | u | q − 2 u , where 1 < q < p and α , β are parameters. First, we show the existence in the resonant case α ∈ σ ( − ∆ p ) for sufficiently large β , thereby generalizing previously known results. The obtained solutions have negative energy. Second, we show the existence for any β > λ 1 ( q ) and sufficiently large α under an additional nonresonant assumption, where λ 1 ( q ) is the first eigenvalue of the q -Laplacian. The obtained solutions have positive energy.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"1 1","pages":"197-208"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83569650","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 Another Type of Transform Called Rangaig Transform 另一种变换叫做Rangaig变换
Differential Equations and Applications Pub Date : 2017-12-19 DOI: 10.12691/IJPDEA-5-1-6
Norodin A. Rangaig, Norhamida D. Minor, G. F. Penonal, Jae Lord Dexter C. Filipinas, V. Convicto
{"title":"On Another Type of Transform Called Rangaig Transform","authors":"Norodin A. Rangaig, Norhamida D. Minor, G. F. Penonal, Jae Lord Dexter C. Filipinas, V. Convicto","doi":"10.12691/IJPDEA-5-1-6","DOIUrl":"https://doi.org/10.12691/IJPDEA-5-1-6","url":null,"abstract":"A new Integral Transform was introduced in this paper. Fundamental properties of this transform were derived and presented such as the convolution identity, and step Heaviside function. It is proven and tested to solve some basic linear-differential equations and had succesfully solved the Abel's Generalized equation and derived the Volterra Integral Equation of the second kind by means of Initial Value Problem. The Natural Logarithm (e.g logex=lnx) has been established and defined by means of modifying the Euler Definite Integral based on the Rangaig's fomulation. Hence, this transform may solve some different kind of integral and differential equations and it competes with other known transforms like Laplace, Sumudu and Elzaki Transform. Keywords: Rangaig Transform, Integral Transform, linear ordinary differential function, Integro-differential equation, Convolution Theorem.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"5 1","pages":"42-48"},"PeriodicalIF":0.0,"publicationDate":"2017-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85401441","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: 4
Optimization of Wealth Investment Strategies for a DC Pension Fund with Stochastic Salary and Extra Contributions 具有随机工资和额外缴费的DC型养老基金财富投资策略优化
Differential Equations and Applications Pub Date : 2017-12-16 DOI: 10.12691/IJPDEA-5-1-5
E. Akpanibah, B. Osu, C. NjokuK.N., Eyo O. Akak
{"title":"Optimization of Wealth Investment Strategies for a DC Pension Fund with Stochastic Salary and Extra Contributions","authors":"E. Akpanibah, B. Osu, C. NjokuK.N., Eyo O. Akak","doi":"10.12691/IJPDEA-5-1-5","DOIUrl":"https://doi.org/10.12691/IJPDEA-5-1-5","url":null,"abstract":"We studied optimal investment strategies for a plan contributor in a defined pension scheme, with stochastic salary and extra contributions, under the affine interest rate model. We considered two cases; where the extra contribution rates are stochastic and constant. We considered investment in three different assets namely risk free asset (cash), zero coupon bonds and the risky asset (stock). Using Legendre transformation method and dual theory, we obtained the optimal investment strategies the three investments using exponential utility function for the two cases. The result shows that the strategies for the respective investments used when there is no extra contribution can be used when the extra contribution rate is constant as in [1] but cannot be used when it is stochastic. Clearly this gives the member and the fund manager good insight on how to invest to maximize profit with minimal risk once this condition arises.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"9 1","pages":"33-41"},"PeriodicalIF":0.0,"publicationDate":"2017-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74651048","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: 7
The Modified Bi-quintic B-spline Base Functions: An Application to Diffusion Equation 修正双五次b样条基函数在扩散方程中的应用
Differential Equations and Applications Pub Date : 2017-08-11 DOI: 10.12691/IJPDEA-5-1-4
S. Kutluay, N. Yağmurlu
{"title":"The Modified Bi-quintic B-spline Base Functions: An Application to Diffusion Equation","authors":"S. Kutluay, N. Yağmurlu","doi":"10.12691/IJPDEA-5-1-4","DOIUrl":"https://doi.org/10.12691/IJPDEA-5-1-4","url":null,"abstract":"In this paper, the bi-quintic B-spline base functions are modified on a general 2-dimensional problem and then they are applied to two-dimensional Diffusion problem in order to obtain its numerical solutions. The computed results are compared with the results given in the literature.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"43 1","pages":"26-32"},"PeriodicalIF":0.0,"publicationDate":"2017-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89961062","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
Solving the Nonlinear Two-Dimension Wave Equation Using Dual Reciprocity Boundary Element Method 用对偶互易边界元法求解非线性二维波动方程
Differential Equations and Applications Pub Date : 2017-06-23 DOI: 10.12691/IJPDEA-5-1-3
Kumars Mahmoodi, H. Ghassemi, A. Heydarian
{"title":"Solving the Nonlinear Two-Dimension Wave Equation Using Dual Reciprocity Boundary Element Method","authors":"Kumars Mahmoodi, H. Ghassemi, A. Heydarian","doi":"10.12691/IJPDEA-5-1-3","DOIUrl":"https://doi.org/10.12691/IJPDEA-5-1-3","url":null,"abstract":"The boundary element method (BEM) is a very effective numerical tool which has been widely applied in engineering problems. Wave equation is a very important equation in applied mathematics with many applications such as wave propagation analysis, acoustics, dynamics, health monitoring and etc. This paper presents to solve the nonlinear 2-D wave equation defined over a rectangular spatial domain with appropriate initial and boundary conditions. Numerical solutions of the governing equations are obtained by using the dual reciprocity boundary element method (DRBEM). Two-dimension wave equation is a time-domain problem, with three independent variables . At the first the Laplace transform is used to reduce by one the number of independent variables (in the present work ), then Salzer's method which is an effective numerical Laplace transform inversion algorithm is used to recover the solution of the original equation at time domain. The present method has been successfully applied to 2-D wave equation with satisfactory accuracy.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"30 1","pages":"19-25"},"PeriodicalIF":0.0,"publicationDate":"2017-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73550089","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: 5
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