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Infinitely many positive solutions for Schrödinger-poisson systems with nonsymmetry potentials 具有非对称势的Schrödinger-poisson系统的无穷多正解
Discrete & Continuous Dynamical Systems - S Pub Date : 2021-01-01 DOI: 10.3934/DCDS.2021054
Fang Qin, Jun Wang, Jing Yang
{"title":"Infinitely many positive solutions for Schrödinger-poisson systems with nonsymmetry potentials","authors":"Fang Qin, Jun Wang, Jing Yang","doi":"10.3934/DCDS.2021054","DOIUrl":"https://doi.org/10.3934/DCDS.2021054","url":null,"abstract":"The present paper deals with a class of Schrodinger-poisson system. Under some suitable assumptions on the decay rate of the coefficients, we derive the existence of infinitely many positive solutions to the problem by using purely variational methods. Comparing to the previous works, we encounter some new challenges because of nonlocal term. By doing some delicate estimates for the nonlocal term we overcome the difficulty and find infinitely many positive solutions.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80106892","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
State feedback for set stabilization of Markovian jump Boolean control networks 马尔可夫跳变布尔控制网络集镇定的状态反馈
Discrete & Continuous Dynamical Systems - S Pub Date : 2021-01-01 DOI: 10.3934/dcdss.2020413
Sanmei Zhu, Jun‐e Feng, Jianli Zhao
{"title":"State feedback for set stabilization of Markovian jump Boolean control networks","authors":"Sanmei Zhu, Jun‐e Feng, Jianli Zhao","doi":"10.3934/dcdss.2020413","DOIUrl":"https://doi.org/10.3934/dcdss.2020413","url":null,"abstract":"In this paper, the set stabilization problem of Markovian jump Boolean control networks (MJBCNs) is investigated via semi-tensor product of matrices. First, the conception of set stabilization is proposed for MJBCNs. Then based on the algebraic expression of MJBCN, a necessary and sufficient condition for set stabilization is provided by a linear programming problem, which is simple to solve. Moreover, by solving this linear programming problem, an algorithm for designing a state feedback controller is developed. Finally, two examples are presented to illustrate the feasibility of the obtained results.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78679553","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
Erratum and addendum to "A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies" (Volume 40, Number 4, 2020, 2285-2313) “远离切线的非奇异自同态的一个正向遍历闭合引理和熵猜想”的勘误和增补(卷40，第4期，2020,2285-2313)
Discrete & Continuous Dynamical Systems - S Pub Date : 2021-01-01 DOI: 10.3934/dcds.2021196
S. Hayashi
{"title":"Erratum and addendum to \"A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies\" (Volume 40, Number 4, 2020, 2285-2313)","authors":"S. Hayashi","doi":"10.3934/dcds.2021196","DOIUrl":"https://doi.org/10.3934/dcds.2021196","url":null,"abstract":"<p style='text-indent:20px;'>We add a lemma implicitly used in the proof of the forward Ergodic Closing Lemma in the paper \"A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies\" [Discrete Contin. Dyn. Syst., <b>40</b> (2020), 2285-2313].</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78732975","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
Galerkin method of weakly damped cubic nonlinear Schrödinger with Dirac impurity, and artificial boundary condition in a half-line 含Dirac杂质的弱阻尼三次非线性Schrödinger的Galerkin方法，以及半线上的人工边界条件
Discrete & Continuous Dynamical Systems - S Pub Date : 2021-01-01 DOI: 10.3934/DCDSS.2021030
A. Chrifi, M. Abounouh, H. A. Moatassime
{"title":"Galerkin method of weakly damped cubic nonlinear Schrödinger with Dirac impurity, and artificial boundary condition in a half-line","authors":"A. Chrifi, M. Abounouh, H. A. Moatassime","doi":"10.3934/DCDSS.2021030","DOIUrl":"https://doi.org/10.3934/DCDSS.2021030","url":null,"abstract":"We consider a weakly damped cubic nonlinear Schrodinger equation with Dirac interaction defect in a half line of begin{document}$ mathbb{R} $end{document} . Endowed with artificial boundary condition at the point begin{document}$ x = 0 $end{document} , we discuss the global existence and uniqueness of solution of this equation by using Faedo–Galerkin method.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"182 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76403678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On the number of limit cycles of a quartic polynomial system 关于一个四次多项式系统的极限环的个数
Discrete & Continuous Dynamical Systems - S Pub Date : 2021-01-01 DOI: 10.3934/dcdss.2020337
Min Li, Maoan Han
{"title":"On the number of limit cycles of a quartic polynomial system","authors":"Min Li, Maoan Han","doi":"10.3934/dcdss.2020337","DOIUrl":"https://doi.org/10.3934/dcdss.2020337","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we consider a quartic polynomial differential system with multiple parameters, and obtain the existence and number of limit cycles with the help of the Melnikov function under perturbation of polynomials of degree <inline-formula><tex-math id=\"M1\">begin{document}$ n = 4 $end{document}</tex-math></inline-formula>.</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"100 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76082974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some new bounds analogous to generalized proportional fractional integral operator with respect to another function 关于另一个函数的一些类似于广义比例分数积分算子的新界
Discrete & Continuous Dynamical Systems - S Pub Date : 2021-01-01 DOI: 10.3934/DCDSS.2021020
S. Rashid, F. Jarad, Z. Hammouch
{"title":"Some new bounds analogous to generalized proportional fractional integral operator with respect to another function","authors":"S. Rashid, F. Jarad, Z. Hammouch","doi":"10.3934/DCDSS.2021020","DOIUrl":"https://doi.org/10.3934/DCDSS.2021020","url":null,"abstract":"<p style='text-indent:20px;'>The present article deals with the new estimates in the view of generalized proportional fractional integral with respect to another function. In the present investigation, we focus on driving certain new classes of integral inequalities utilizing a family of positive functions <inline-formula><tex-math id=\"M1\">begin{document}$ n(ninmathbb{N}) $end{document}</tex-math></inline-formula> for this newly defined operator. From the computed outcomes, we concluded some new variants for classical generalized proportional fractional and other integrals as remarks. These variants are connected with some existing results in the literature. Certain interesting consequent results of the main theorems are also pointed out.</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"132 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88819526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
High and low perturbations of Choquard equations with critical reaction and variable growth 具有临界反应和变增长的Choquard方程的高低摄动
Discrete & Continuous Dynamical Systems - S Pub Date : 2021-01-01 DOI: 10.3934/dcds.2021180
Youpei Zhang, Xianhua Tang, V. Rǎdulescu
{"title":"High and low perturbations of Choquard equations with critical reaction and variable growth","authors":"Youpei Zhang, Xianhua Tang, V. Rǎdulescu","doi":"10.3934/dcds.2021180","DOIUrl":"https://doi.org/10.3934/dcds.2021180","url":null,"abstract":"<p style='text-indent:20px;'>We are concerned with the existence of ground state solutions to the nonhomogeneous perturbed Choquard equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ - Delta_{p(x)} u + V(x)|u|^{p(x) - 2} u $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE2\"> begin{document}$ = left( int_{mathbb R^N} r(y)^{-1}|u(y)|^{r(y)}|x-y|^{-lambda(x,y)} dyright) |u|^{r(x)-2} u+g(x,u) mbox{in} mathbb R^N, $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where the exponent <inline-formula><tex-math id=\"M1\">begin{document}$ r(cdot) $end{document}</tex-math></inline-formula> is critical with respect to the Hardy-Littlewood-Sobolev inequality for variable exponents. We first consider the case where the perturbation <inline-formula><tex-math id=\"M2\">begin{document}$ g(cdot ,cdot) $end{document}</tex-math></inline-formula> is subcritical and we distinguish between the superlinear and sublinear cases. In both situations we establish the existence of solutions and we prove the asymptotic behavior of low-energy solutions in the case of high perturbations. Next, we study the case where the nonlinearity <inline-formula><tex-math id=\"M3\">begin{document}$ g(cdot ,cdot) $end{document}</tex-math></inline-formula> is critical. We prove the existence of solutions both for low and high perturbations and we establish asymptotic properties of low-energy solutions.</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80571772","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
Forward untangling and applications to the uniqueness problem for the continuity equation 前向解结及其在连续性方程唯一性问题中的应用
Discrete & Continuous Dynamical Systems - S Pub Date : 2021-01-01 DOI: 10.3934/dcds.2020384
S. Bianchini, P. Bonicatto
{"title":"Forward untangling and applications to the uniqueness problem for the continuity equation","authors":"S. Bianchini, P. Bonicatto","doi":"10.3934/dcds.2020384","DOIUrl":"https://doi.org/10.3934/dcds.2020384","url":null,"abstract":"We introduce the notion of forward untangled Lagrangian representation of a measuredivergence vector-measure ρ(1, b), where ρ ∈ M+(Rd+1) and b : Rd+1 → Rd is a ρ-integrable vector field with divt,x(ρ(1, b)) = μ ∈ M(R × Rd): forward untangling formalizes the notion of forward uniqueness in the language of Lagrangian representations. We identify local conditions for a Lagrangian representation to be forward untangled, and we show how to derive global forward untangling from such local assumptions. We then show how to reduce the PDE divt,x(ρ(1, b)) = μ on a partition of R+ × Rd obtained concatenating the curves seen by the Lagrangian representation. As an application, we recover known well posedeness results for the flow of monotone vector fields and for the associated continuity equation.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"194 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83732866","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
Observer-based control for a class of hybrid linear and nonlinear systems 一类线性和非线性混合系统的观测器控制
Discrete & Continuous Dynamical Systems - S Pub Date : 2021-01-01 DOI: 10.3934/dcdss.2020376
A. Alessandri, F. Bedouhene, D. Bouhadjra, A. Zemouche, P. Bagnerini
{"title":"Observer-based control for a class of hybrid linear and nonlinear systems","authors":"A. Alessandri, F. Bedouhene, D. Bouhadjra, A. Zemouche, P. Bagnerini","doi":"10.3934/dcdss.2020376","DOIUrl":"https://doi.org/10.3934/dcdss.2020376","url":null,"abstract":"An approach to output feedback control for hybrid discrete-time systems subject to uncertain mode transitions is proposed. The system dynamics may assume different modes upon the occurrence of a switching that is not directly measurable. Since the current system mode is unknown, a regulation scheme is proposed by combining a Luenberger observer to estimate the continuous state, a mode estimator, and a controller fed with the estimates of both continuous state variables and mode. The closed-loop stability is ensured under suitable conditions given in terms of linear matrix inequalities. Since complexity and conservativeness grow with the increase of the modes, we address the problem of reducing the number of linear matrix inequalities by providing more easily tractable stability conditions. Such conditions are extended to deal with systems having also Lipschitz nonlinearities and affected by disturbances. The effectiveness of the proposed approach is shown by means of simulations.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"174 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79654864","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
Stability and bifurcation analysis in a delay-induced predator-prey model with Michaelis-Menten type predator harvesting Michaelis-Menten型捕食者捕获延迟诱导捕食者-猎物模型的稳定性和分岔分析
Discrete & Continuous Dynamical Systems - S Pub Date : 2021-01-01 DOI: 10.3934/dcdss.2020259
Ming Liu, Dongpo Hu, F. Meng
{"title":"Stability and bifurcation analysis in a delay-induced predator-prey model with Michaelis-Menten type predator harvesting","authors":"Ming Liu, Dongpo Hu, F. Meng","doi":"10.3934/dcdss.2020259","DOIUrl":"https://doi.org/10.3934/dcdss.2020259","url":null,"abstract":"The present paper considers a delay-induced predator-prey model with Michaelis-Menten type predator harvesting. The existence of the nontrivial positive equilibria is discussed, and some sufficient conditions for locally asymptotically stability of one of the positive equilibria are developed. Meanwhile, the existence of Hopf bifurcation is discussed by choosing time delays as the bifurcation parameters. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out to support the analytical results.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81178576","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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