In this work, we study the oscillation and nonoscillation properties of a class of second order neutral impulsive differential equations with constant coefficients and constant delays by using pulsatile constant. Also, an attempt is made to extend the constant coefficient results to variable coefficient equations.
{"title":"Characterization of a class of second order neutral impulsive systems via pulsatile constant","authors":"A. Tripathy, S. Santra","doi":"10.7153/DEA-09-07","DOIUrl":"https://doi.org/10.7153/DEA-09-07","url":null,"abstract":"In this work, we study the oscillation and nonoscillation properties of a class of second order neutral impulsive differential equations with constant coefficients and constant delays by using pulsatile constant. Also, an attempt is made to extend the constant coefficient results to variable coefficient equations.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"73 1","pages":"87-98"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86605790","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 study some new nonlinear boundary value problems of LiouvilleCaputo type fractional differential equations supplemented with nonlocal multi-point conditions involving lower order fractional derivative. We make use of some well known tools of the fixed point theory to establish the existence of solutions for problems at hand. For illustration of the obtained results, several examples are discussed. Mathematics subject classification (2010): 34A08, 34B15.
{"title":"On nonlinear fractional-order boundary value problems with nonlocal multi-point conditions involving Liouville-Caputo derivative","authors":"R. Agarwal, A. Alsaedi, A. Alsharif, B. Ahmad","doi":"10.7153/DEA-09-12","DOIUrl":"https://doi.org/10.7153/DEA-09-12","url":null,"abstract":"In this paper, we study some new nonlinear boundary value problems of LiouvilleCaputo type fractional differential equations supplemented with nonlocal multi-point conditions involving lower order fractional derivative. We make use of some well known tools of the fixed point theory to establish the existence of solutions for problems at hand. For illustration of the obtained results, several examples are discussed. Mathematics subject classification (2010): 34A08, 34B15.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"83 1","pages":"147-160"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83481160","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 note we use an oscillatory theorem for the second order linear ordinary differential equation in order to establish an oscillatory criterion for the generalized Hill’s equation. We formulate a hypothesis about representation of the sum of periodic functions with rational dependent periods by a sum of periodic functions with rational independent periods.
{"title":"A new oscillatory criterion for the generalized Hill's equation","authors":"G. Grigorian","doi":"10.7153/DEA-2017-09-26","DOIUrl":"https://doi.org/10.7153/DEA-2017-09-26","url":null,"abstract":"In this note we use an oscillatory theorem for the second order linear ordinary differential equation in order to establish an oscillatory criterion for the generalized Hill’s equation. We formulate a hypothesis about representation of the sum of periodic functions with rational dependent periods by a sum of periodic functions with rational independent periods.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"22 1","pages":"369-377"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90954048","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}
{"title":"The (p,q)-elliptic systems with concave-convex nonlinearities","authors":"Xia Liu, Z. Ou","doi":"10.7153/dea-2017-09-35","DOIUrl":"https://doi.org/10.7153/dea-2017-09-35","url":null,"abstract":"","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"7 1","pages":"521-531"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73526933","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}
An ordinary differential system, referred to as Lanchester-type model, is treated. We examine how asymptotic behavior of every solution of the system varies according to the initial data. We can show the existence of critical values for initial data.
{"title":"Asymptotic behavior of positive solutions of a Lanchester-type model","authors":"Tran Thi Nha Trang, H. Usami","doi":"10.7153/dea-09-19","DOIUrl":"https://doi.org/10.7153/dea-09-19","url":null,"abstract":"An ordinary differential system, referred to as Lanchester-type model, is treated. We examine how asymptotic behavior of every solution of the system varies according to the initial data. We can show the existence of critical values for initial data.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"61 1","pages":"241-252"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75633042","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}
The aim of this paper is to give some Ulam-Hyers-Rassias stability results for Volterratype stochastic integral equations. The argument makes use of Gronwall lemma and Banach’s fixed point theorem. Mathematics subject classification (2010): 60H20, 34K20, 26D10, 46C05.
{"title":"Ulam-Hyers-Rassias stability of a nonlinear stochastic integral equation of Volterra type","authors":"Ngo Phuoc Nguyen Ngoc","doi":"10.7153/DEA-09-15","DOIUrl":"https://doi.org/10.7153/DEA-09-15","url":null,"abstract":"The aim of this paper is to give some Ulam-Hyers-Rassias stability results for Volterratype stochastic integral equations. The argument makes use of Gronwall lemma and Banach’s fixed point theorem. Mathematics subject classification (2010): 60H20, 34K20, 26D10, 46C05.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"9 1","pages":"183-193"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82631177","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 present a result on existence of exponential attractors for abstract random dynamical systems, and then give a criterion for exponentially attractive property of random attractors. As an application, we first prove that the random dynamical system generated by a stochastic reaction-diffusion equation possesses a random exponential attractor. Then we show that the unique random equilibrium when the nonlinearity satisfies some restrictive condition is exactly an exponential attractor.
{"title":"Random Exponential Attractor and Equilibrium for a Stochastic Reaction-diffusion Equation with Multiplicative Noise","authors":"Gangwei Wang","doi":"10.12691/ijpdea-4-2-2","DOIUrl":"https://doi.org/10.12691/ijpdea-4-2-2","url":null,"abstract":"In this paper, we present a result on existence of exponential attractors for abstract random dynamical systems, and then give a criterion for exponentially attractive property of random attractors. As an application, we first prove that the random dynamical system generated by a stochastic reaction-diffusion equation possesses a random exponential attractor. Then we show that the unique random equilibrium when the nonlinearity satisfies some restrictive condition is exactly an exponential attractor.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"27 1","pages":"25-31"},"PeriodicalIF":0.0,"publicationDate":"2016-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82793616","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}
Option price and random arbitrage returns change on different time scales allow the development of an asymptotic pricing theory involving the options rather than exact prices. The role that random arbitrage opportunities play in pricing financial derivatives can be determined. In this paper, we construct Green’s functions for terminal boundary value problems of the fractional Black-Scholes equation. We follow further an approach suggested in literature and focus on the pricing bands for options that account for random arbitrage opportunities and got similar result for the fractional Black- Scholes option pricing.
{"title":"Fractional Black Scholes Option Pricing with Stochastic Arbitrage Return","authors":"B. Osu, Chukwunezu A. Ifeoma","doi":"10.12691/ijpdea-4-2-1","DOIUrl":"https://doi.org/10.12691/ijpdea-4-2-1","url":null,"abstract":"Option price and random arbitrage returns change on different time scales allow the development of an asymptotic pricing theory involving the options rather than exact prices. The role that random arbitrage opportunities play in pricing financial derivatives can be determined. In this paper, we construct Green’s functions for terminal boundary value problems of the fractional Black-Scholes equation. We follow further an approach suggested in literature and focus on the pricing bands for options that account for random arbitrage opportunities and got similar result for the fractional Black- Scholes option pricing.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"43 1","pages":"20-24"},"PeriodicalIF":0.0,"publicationDate":"2016-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77411268","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}
As the B-spline method was developed for solving higher order differential equations, we present a brief survey to construct a higher degree B-spline. The new technique has been given in this field, accordingly a numerical illustration used to solve boundary value problems by employ quintic B-spline function. An example has been given for calculating maximum absolute error through n nodes.
{"title":"Employment Higher Degree B-Spline Function for Solving Higher Order Differential Equations","authors":"K. Jwamer, I. N. Abdullah","doi":"10.12691/IJPDEA-4-1-3","DOIUrl":"https://doi.org/10.12691/IJPDEA-4-1-3","url":null,"abstract":"As the B-spline method was developed for solving higher order differential equations, we present a brief survey to construct a higher degree B-spline. The new technique has been given in this field, accordingly a numerical illustration used to solve boundary value problems by employ quintic B-spline function. An example has been given for calculating maximum absolute error through n nodes.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"49 1","pages":"16-19"},"PeriodicalIF":0.0,"publicationDate":"2016-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83717672","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 is concerned with the three dimensional motion of a nonlinear dynamical system. The motion is described by nonlinear partial differential equation, which is converted by Galerkin method to three dimensional ordinary differential equations. The three dimensional differential equations, under the influence of external forces, are solved analytically and numerically by the multiple time scales perturbation technique and the Runge-Kutta fourth order method. Phase plane technique and frequency response equations are used to investigate the stability of the system and the effects of the parameters of the system, respectively.
{"title":"Harmonic Oscillations and Resonances in 3-D Nonlinear Dynamical System","authors":"Usama H. Hegazy, Mousa A. ALshawish","doi":"10.12691/IJPDEA-4-1-2","DOIUrl":"https://doi.org/10.12691/IJPDEA-4-1-2","url":null,"abstract":"This paper is concerned with the three dimensional motion of a nonlinear dynamical system. The motion is described by nonlinear partial differential equation, which is converted by Galerkin method to three dimensional ordinary differential equations. The three dimensional differential equations, under the influence of external forces, are solved analytically and numerically by the multiple time scales perturbation technique and the Runge-Kutta fourth order method. Phase plane technique and frequency response equations are used to investigate the stability of the system and the effects of the parameters of the system, respectively.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"19 1","pages":"7-15"},"PeriodicalIF":0.0,"publicationDate":"2016-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82193297","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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