The aim of this work is to present a novel approach based on the artificial neural network for finding the numerical solution of first order fuzzy differential equations under generalized H-derivation. The differentiability concept used in this paper is the generalized differentiability since a fuzzy differential equation under this differentiability can have two solutions. The fuzzy trial solution of fuzzy initial value problem is written as a sum of two parts. The first part satisfies the fuzzy condition, it contains no adjustable parameters. The second part involves feed-forward neural networks containing adjustable parameters. Under some conditions the proposed method provides numerical solutions with high accuracy.
{"title":"Artificial Neural Network for Solving Fuzzy Differential Equations under Generalized H – Derivation","authors":"M. H. Suhhiem","doi":"10.12691/IJPDEA-5-1-1","DOIUrl":"https://doi.org/10.12691/IJPDEA-5-1-1","url":null,"abstract":"The aim of this work is to present a novel approach based on the artificial neural network for finding the numerical solution of first order fuzzy differential equations under generalized H-derivation. The differentiability concept used in this paper is the generalized differentiability since a fuzzy differential equation under this differentiability can have two solutions. The fuzzy trial solution of fuzzy initial value problem is written as a sum of two parts. The first part satisfies the fuzzy condition, it contains no adjustable parameters. The second part involves feed-forward neural networks containing adjustable parameters. Under some conditions the proposed method provides numerical solutions with high accuracy.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"75 1","pages":"1-9"},"PeriodicalIF":0.0,"publicationDate":"2017-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86288430","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}
S. Lecheheb, Hakim Lakhal, Maouni Messaoud, K. Slimani
In this article, we are interested in the study of the existence of weak solutions of boundary value problem for the nonlinear elliptic system , where Ω is a bounded domain in and are continuous functions . We use the Leray-Schauder degree theory under not linear for the three reasons: the terms of diffusion, convection and reaction, and the following condition on the last term f and and
{"title":"Study of a System of Convection-Diffusion-Reaction","authors":"S. Lecheheb, Hakim Lakhal, Maouni Messaoud, K. Slimani","doi":"10.12691/IJPDEA-4-2-3","DOIUrl":"https://doi.org/10.12691/IJPDEA-4-2-3","url":null,"abstract":"In this article, we are interested in the study of the existence of weak solutions of boundary value problem for the nonlinear elliptic system , where Ω is a bounded domain in and are continuous functions . We use the Leray-Schauder degree theory under not linear for the three reasons: the terms of diffusion, convection and reaction, and the following condition on the last term f and and","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"34 1","pages":"32-37"},"PeriodicalIF":0.0,"publicationDate":"2017-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77547552","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 provide a direct proof of a result comparing the area functions of solutions of two second order linear elliptic operators, when the discrepancy between their main coefficients is supported on Whitney type cubes of the unit ball of n dimensional Euclidean space. Our arguments are specialized to this type of operators, and the vanishing Carleson condition that we adopt is inspired by work of C. Sweezy. The comparison between area functions implies the preservation of the so called exponential square theorem assuming the aforementioned discrepancy of the coefficients. Mathematics subject classification (2010): 42B25, 42B35, 31A20.
{"title":"Area integrals and the exponential square theorem for elliptic operators with coefficients supported in Whitney type cubes","authors":"Marysol Navarro-Burruel, J. Rivera-Noriega","doi":"10.7153/DEA-2017-09-23","DOIUrl":"https://doi.org/10.7153/DEA-2017-09-23","url":null,"abstract":"We provide a direct proof of a result comparing the area functions of solutions of two second order linear elliptic operators, when the discrepancy between their main coefficients is supported on Whitney type cubes of the unit ball of n dimensional Euclidean space. Our arguments are specialized to this type of operators, and the vanishing Carleson condition that we adopt is inspired by work of C. Sweezy. The comparison between area functions implies the preservation of the so called exponential square theorem assuming the aforementioned discrepancy of the coefficients. Mathematics subject classification (2010): 42B25, 42B35, 31A20.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"13 1","pages":"311-325"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86944934","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}
Cholticha Nuchpong, S. Ntouyas, P. Thiramanus, J. Tariboon
In this paper, we investigate the asymptotic behavior of solutions for a class of mixed type impulsive neutral delay differential equations with constant jumps. Sufficient conditions are given to guarantee that every non-oscillatory solution of the system tends to zero as t → ∞ . An example illustrating the result is also presented.
{"title":"Asymptotic behavior of solutions of impulsive neutral differential equations with constant jumps","authors":"Cholticha Nuchpong, S. Ntouyas, P. Thiramanus, J. Tariboon","doi":"10.7153/DEA-09-20","DOIUrl":"https://doi.org/10.7153/DEA-09-20","url":null,"abstract":"In this paper, we investigate the asymptotic behavior of solutions for a class of mixed type impulsive neutral delay differential equations with constant jumps. Sufficient conditions are given to guarantee that every non-oscillatory solution of the system tends to zero as t → ∞ . An example illustrating the result is also presented.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"4 1","pages":"263-264"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83261614","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 [15], Wei solved a delay differential equation on the half-line. The current paper is an extension of these results to the set-valued case. The results involve measurable selections and the contraction mapping theorem for set-valued functions.
{"title":"Solutions for a second-order Delay differential inclusion on the half-line with boundary values","authors":"John S. Spraker","doi":"10.7153/DEA-2017-09-37","DOIUrl":"https://doi.org/10.7153/DEA-2017-09-37","url":null,"abstract":"In [15], Wei solved a delay differential equation on the half-line. The current paper is an extension of these results to the set-valued case. The results involve measurable selections and the contraction mapping theorem for set-valued functions.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"33 1","pages":"543-552"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81290183","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":"Multiple positive solutions for nonlocal boundary value problems with p-Laplacian operator","authors":"Sheng-Ping Wang","doi":"10.7153/dea-2017-09-36","DOIUrl":"https://doi.org/10.7153/dea-2017-09-36","url":null,"abstract":"","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"83 1","pages":"533-542"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81077771","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 a Choquard equation involving both concave-convex and Hardy-Littlewood-Sobolev critical exponent. By using the N ehari manifold, fibering maps and the Lusternik-Schnirelman category, we prove that the problem has at least cat(Ω)+ 1 distinct positive solutions.
{"title":"Multiple positive solutions for a Choquard equation involving both concave-convex and Hardy-Littlewood-Sobolev critical exponent","authors":"R. Echarghaoui, M. Khiddi, S. Sbai","doi":"10.7153/DEA-2017-09-34","DOIUrl":"https://doi.org/10.7153/DEA-2017-09-34","url":null,"abstract":"In this paper, we consider a Choquard equation involving both concave-convex and Hardy-Littlewood-Sobolev critical exponent. By using the N ehari manifold, fibering maps and the Lusternik-Schnirelman category, we prove that the problem has at least cat(Ω)+ 1 distinct positive solutions.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"71 1","pages":"505-520"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81584674","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 the existence of infinitely many periodic solutions to a class of perturbed second-order impulsive Hamiltonian systems. Our approach is based on variational methods and critical point theory.
研究了一类扰动二阶脉冲哈密顿系统无穷多个周期解的存在性。我们的方法是基于变分方法和临界点理论。
{"title":"Infinitely many periodic solutions to a class of perturbed second-order impulsive Hamiltonian systems","authors":"J. Graef, S. Heidarkhani, L. Kong","doi":"10.7153/DEA-09-16","DOIUrl":"https://doi.org/10.7153/DEA-09-16","url":null,"abstract":"We investigate the existence of infinitely many periodic solutions to a class of perturbed second-order impulsive Hamiltonian systems. Our approach is based on variational methods and critical point theory.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"9 1","pages":"195-212"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83463335","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, we obtain a new formula which generalizes the Liouville formula of the linear differential system to nonlinear differential system. We establish the relationship between the Jacobi determinant of the first integral and the trace of Jacobi matrix of the n -dimensional vector field.
{"title":"On a generalization of the Liouville formula","authors":"Zhengyong Zhou, L. Xie","doi":"10.7153/DEA-09-17","DOIUrl":"https://doi.org/10.7153/DEA-09-17","url":null,"abstract":"In this article, we obtain a new formula which generalizes the Liouville formula of the linear differential system to nonlinear differential system. We establish the relationship between the Jacobi determinant of the first integral and the trace of Jacobi matrix of the n -dimensional vector field.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"123 1","pages":"213-217"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85651658","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 establish a minimization principle in an ordered Banach space (in particular in a Riesz-Banach space). As an application we discuss the existence of a positive solution for a boundary value problem on the half-line even when the nonlinear term is signchanging. Mathematics subject classification (2010): 35B38, 47L07.
{"title":"Minimization principle in ordered Banach spaces and application via Ekeland's variational principle","authors":"A. Boucenna, M. Briki, T. Moussaoui, D. Regan","doi":"10.7153/dea-09-08","DOIUrl":"https://doi.org/10.7153/dea-09-08","url":null,"abstract":"In this paper we establish a minimization principle in an ordered Banach space (in particular in a Riesz-Banach space). As an application we discuss the existence of a positive solution for a boundary value problem on the half-line even when the nonlinear term is signchanging. Mathematics subject classification (2010): 35B38, 47L07.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"28 6","pages":"99-104"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91498546","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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