In this paper, we present three results about the existence of solutions to discontinuous dynamic equations on time scales. The existence of Carathéodory type solution is produced using convergence and Arzela–Ascoli theorem. The Banach’s fixed point theorem is used to investigate the existence and uniqueness of solutions and using Schaefer’s fixed point theorem we establish the existence of at least one solution. Our results generalizes and extends some existing theorems in this field. Mathematics subject classification (2010): 26E70, 34A36, 34N05.
{"title":"Existence results for solutions to discontinuous dynamic equations on time scales","authors":"Sanket Tikare, I. Santos","doi":"10.7153/DEA-2020-12-06","DOIUrl":"https://doi.org/10.7153/DEA-2020-12-06","url":null,"abstract":"In this paper, we present three results about the existence of solutions to discontinuous dynamic equations on time scales. The existence of Carathéodory type solution is produced using convergence and Arzela–Ascoli theorem. The Banach’s fixed point theorem is used to investigate the existence and uniqueness of solutions and using Schaefer’s fixed point theorem we establish the existence of at least one solution. Our results generalizes and extends some existing theorems in this field. Mathematics subject classification (2010): 26E70, 34A36, 34N05.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"10 40 1","pages":"89-100"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87229830","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 studied. Asymptotic properties of solutions for such systems are considered. In particular, we examine how the limit of the solution as time tends to the infinity varies according to the initial data and we find asymptotic form of solutions that decay to (0,0) . Mathematics subject classification (2010): 34C11, 35E10.
{"title":"Asymptotic properties of solutions of a Lanchester-type model","authors":"Takahiro Ito, T. Ogiwara, H. Usami","doi":"10.7153/DEA-2020-12-01","DOIUrl":"https://doi.org/10.7153/DEA-2020-12-01","url":null,"abstract":"An ordinary differential system referred to as Lanchester-type model is studied. Asymptotic properties of solutions for such systems are considered. In particular, we examine how the limit of the solution as time tends to the infinity varies according to the initial data and we find asymptotic form of solutions that decay to (0,0) . Mathematics subject classification (2010): 34C11, 35E10.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"1206 1","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80026617","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 consider the existence of antisymmetric solutions for the generalized quasilinear Schrödinger equation in H1(RN) :
本文考虑H1(RN)中广义拟线性Schrödinger方程的反对称解的存在性:
{"title":"Antisymmetric solutions for a class generalized quasilinear Schrödinger equations","authors":"Janete Soares Gamboa, Jiazheng Zhou","doi":"10.7153/DEA-2020-12-03","DOIUrl":"https://doi.org/10.7153/DEA-2020-12-03","url":null,"abstract":"In this paper we consider the existence of antisymmetric solutions for the generalized quasilinear Schrödinger equation in H1(RN) :","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"2 1","pages":"29-45"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88739875","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 work introduce a difference controls of players by using a new control method to completing a pursuit game. We study pursuit game problems for controlled partial differential equations of the parabolic type. We proved a theorem on pursuit game with mixed constraints, where pursuers control are subjected to integral (geometric) constraint and geometric (integral) constraint are imposed on evaders control. Moreover, we established the sufficient conditions for which pursuit is possible in the game considered.
{"title":"A Problem of Pursuit Game with Various Constraints on Controls of Players","authors":"F. Allahabi, M. A. Mahiub","doi":"10.12691/IJPDEA-6-1-2","DOIUrl":"https://doi.org/10.12691/IJPDEA-6-1-2","url":null,"abstract":"This work introduce a difference controls of players by using a new control method to completing a pursuit game. We study pursuit game problems for controlled partial differential equations of the parabolic type. We proved a theorem on pursuit game with mixed constraints, where pursuers control are subjected to integral (geometric) constraint and geometric (integral) constraint are imposed on evaders control. Moreover, we established the sufficient conditions for which pursuit is possible in the game considered.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"31 1","pages":"13-17"},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84684465","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 work is to analyze the stock market using the solution of the fractional option pricing model as in literature. First, the Hurst exponent of the stock prices of two different stock index using Detrended Fluctuation Analysis (DFA) method was estimated. A program using MATLAB code was written which is used to calculate the Hurst exponent, the volatility, the discount rate, the call and put options prices efficiently so as to save time and avoid computational errors which may arise through manual computation.
{"title":"Analyzing the Stock Market Using the Solution of the Fractional Option Pricing Model","authors":"O. OsuB., I. ChukwunezuA., C. Olunkwa, N. Obi.C.","doi":"10.12691/IJPDEA-6-1-1","DOIUrl":"https://doi.org/10.12691/IJPDEA-6-1-1","url":null,"abstract":"The aim of this work is to analyze the stock market using the solution of the fractional option pricing model as in literature. First, the Hurst exponent of the stock prices of two different stock index using Detrended Fluctuation Analysis (DFA) method was estimated. A program using MATLAB code was written which is used to calculate the Hurst exponent, the volatility, the discount rate, the call and put options prices efficiently so as to save time and avoid computational errors which may arise through manual computation.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"122 1","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"2019-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76387283","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 presents some sufficient conditions for the existence of solutions of fractional differential equation with nonlocal multi-point boundary conditions involving Caputo fractional derivative and integral boundary conditions. Our analysis relies on the Banach contraction principle, Boyd and Wong fixed point theorem, Leray-Schauder nonlinear alternative. Finally, examples are provided to illustrate our main results.
{"title":"On the existence and uniqueness of solutions for fractional differential equations with nonlocal multi-point boundary conditions","authors":"Faouzi Haddouchi","doi":"10.7153/DEA-2021-13-13","DOIUrl":"https://doi.org/10.7153/DEA-2021-13-13","url":null,"abstract":"This paper presents some sufficient conditions for the existence of solutions of fractional differential equation with nonlocal multi-point boundary conditions involving Caputo fractional derivative and integral boundary conditions. Our analysis relies on the Banach contraction principle, Boyd and Wong fixed point theorem, Leray-Schauder nonlinear alternative. Finally, examples are provided to illustrate our main results.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"963 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77074375","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 prove a coupled hybrid fixed point theorem involving the sum of two coupled operators in a partially ordered Banach space and apply to a pair of nonlinear second order coupled linearly perturbed hybrid differential equations with the periodic boundary conditions for proving the existence and approximation of coupled solutions under certain mixed hybrid conditions. The abstract existence result of the coupled periodic boundary value problems is also illustrated by furnishing a numerical example.
{"title":"A coupled hybrid fixed point theorem involving the sum of two coupled operators in a partially ordered Banach space with applications","authors":"B. Dhage","doi":"10.7153/DEA-2017-09-31","DOIUrl":"https://doi.org/10.7153/DEA-2017-09-31","url":null,"abstract":"In this paper we prove a coupled hybrid fixed point theorem involving the sum of two coupled operators in a partially ordered Banach space and apply to a pair of nonlinear second order coupled linearly perturbed hybrid differential equations with the periodic boundary conditions for proving the existence and approximation of coupled solutions under certain mixed hybrid conditions. The abstract existence result of the coupled periodic boundary value problems is also illustrated by furnishing a numerical example.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"52 1","pages":"453-477"},"PeriodicalIF":0.0,"publicationDate":"2018-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90626580","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 plant pest mathematical model is presented with integrated pest management through impulse. Two control measures: Biological(Natural Enemies) and Chemical pesticides are taken in consideration in the model through impulse. Boundedness and the sufficient conditions of existence of the positive periodic solutions is established. Further, the local stability of the pest extinction equilibrium point is studied using Floquet’s theory. It is proved that the pest extinction equilibrium point is globally stable at T < Tmax and the system is permanent for T > Tmax . Numerical data per week are taken to illustrate the theoretical results using MATLAB software.
{"title":"Plant-Pest-natural enemy model with impulsive biological and chemical control","authors":"V. Kumari, Sudipa Chauhan, S. Bhatia, J. Dhar","doi":"10.7153/dea-2018-10-28","DOIUrl":"https://doi.org/10.7153/dea-2018-10-28","url":null,"abstract":"In this paper, a plant pest mathematical model is presented with integrated pest management through impulse. Two control measures: Biological(Natural Enemies) and Chemical pesticides are taken in consideration in the model through impulse. Boundedness and the sufficient conditions of existence of the positive periodic solutions is established. Further, the local stability of the pest extinction equilibrium point is studied using Floquet’s theory. It is proved that the pest extinction equilibrium point is globally stable at T < Tmax and the system is permanent for T > Tmax . Numerical data per week are taken to illustrate the theoretical results using MATLAB software.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"16 1","pages":"413-431"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79785022","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, by using the classical Banach contraction principle, we investigate and establish the stability in the sense of Ulam-Hyers and in the sense of Ulam-Hyers-Rassias for the following stochastic integral equation Xt = ξt + ∫ t 0 A(t,s,Xs)ds+ ∫ t 0 B(t,s,Xs)dWs, where ∫ t 0 B(t,s,Xs)dWs is Ito integral.
{"title":"Ulam-Hyers-Rassias stability of a nonlinear stochastic Ito-Volterra integral equation","authors":"Ngo Phuoc Nguyen Ngoc, N. Vinh","doi":"10.7153/DEA-2018-10-27","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-27","url":null,"abstract":"In this paper, by using the classical Banach contraction principle, we investigate and establish the stability in the sense of Ulam-Hyers and in the sense of Ulam-Hyers-Rassias for the following stochastic integral equation Xt = ξt + ∫ t 0 A(t,s,Xs)ds+ ∫ t 0 B(t,s,Xs)dWs, where ∫ t 0 B(t,s,Xs)dWs is Ito integral.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"6 1","pages":"397-411"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76975124","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 article it is shown that linear elliptic PDEs admit very weak solutions for rather singular data – like non-integrable right hand sides or singular Neumann boundary conditions – not only in case of continuous coefficients, but even for general bounded measurable coefficients. This is rather astonishing, as under such weak assumptions on the coefficients generally strong solutions do not exist, thus the duality between very weak solutions and strong solutions seems to indicate that very weak solutions do not exist either. We circumvent this problem by using an appropriate functional analytic setting and particularly Hölder continuity of weak solutions established by de Giorgi Nash Moser to obtain existence of very weak solutions to singular data for irregular coefficients.
{"title":"Very weak solutions of linear elliptic PDEs with singular data and irregular coefficients","authors":"J. Merker","doi":"10.7153/DEA-2018-10-02","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-02","url":null,"abstract":"In this article it is shown that linear elliptic PDEs admit very weak solutions for rather singular data – like non-integrable right hand sides or singular Neumann boundary conditions – not only in case of continuous coefficients, but even for general bounded measurable coefficients. This is rather astonishing, as under such weak assumptions on the coefficients generally strong solutions do not exist, thus the duality between very weak solutions and strong solutions seems to indicate that very weak solutions do not exist either. We circumvent this problem by using an appropriate functional analytic setting and particularly Hölder continuity of weak solutions established by de Giorgi Nash Moser to obtain existence of very weak solutions to singular data for irregular coefficients.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"6 1","pages":"3-20"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81118142","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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