AIMS Mathematics最新文献

{"title":"Existence and concentration of solutions for a Kirchhoff-type problem with sublinear perturbation and steep potential well","authors":"Shuwen He, Xiaobo Wen","doi":"10.3934/math.2023325","DOIUrl":"https://doi.org/10.3934/math.2023325","url":null,"abstract":"<abstract><p>In this paper, we consider the following nonlinear Kirchhoff-type problem with sublinear perturbation and steep potential well</p> <p><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ begin{eqnarray*} left {begin{array}{ll} -Big(a+bint_{mathbb{R}^3}|nabla u|^2dxBig)Delta u+lambda V(x)u = f(x,u)+g(x)|u|^{q-2}u mbox{in} mathbb{R}^3, uin H^1(mathbb{R}^3), end{array} right. label{1} end{eqnarray*} $end{document} </tex-math></disp-formula></p> <p>where $ a $ and $ b $ are positive constants, $ lambda > 0 $ is a parameter, $ 1 < q < 2 $, the potential $ Vin C(mathbb{R}^3, mathbb{R}) $ and $ V^{-1}(0) $ has a nonempty interior. The functions $ f $ and $ g $ are assumed to obey a certain set of conditions. The existence of two nontrivial solutions are obtained by using variational methods. Furthermore, the concentration behavior of solutions as $ lambdarightarrow infty $ is also explored.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70178463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simulation analysis, properties and applications on a new Burr XII model based on the Bell-X functionalities","authors":"A. Alanzi, Muhammad Imran, Muhammad Mohsin Tahir, C. Chesneau, Farrukh Jamal, Saima Shakoor, Waqas Sami","doi":"10.3934/math.2023352","DOIUrl":"https://doi.org/10.3934/math.2023352","url":null,"abstract":"In this article, we make mathematical and practical contributions to the Bell-X family of absolutely continuous distributions. As a main member of this family, a special distribution extending the modeling perspectives of the famous Burr XII (BXII) distribution is discussed in detail. It is called the Bell-Burr XII (BBXII) distribution. It stands apart from the other extended BXII distributions because of its flexibility in terms of functional shapes. On the theoretical side, a linear representation of the probability density function and the ordinary and incomplete moments are among the key properties studied in depth. Some commonly used entropy measures, namely Rényi, Havrda and Charvat, Arimoto, and Tsallis entropy, are derived. On the practical (inferential) side, the associated parameters are estimated using seven different frequentist estimation methods, namely the methods of maximum likelihood estimation, percentile estimation, least squares estimation, weighted least squares estimation, Cramér von-Mises estimation, Anderson-Darling estimation, and right-tail Anderson-Darling estimation. A simulation study utilizing all these methods is offered to highlight their effectiveness. Subsequently, the BBXII model is successfully used in comparisons with other comparable models to analyze data on patients with acute bone cancer and arthritis pain. A group acceptance sampling plan for truncated life tests is also proposed when an item's lifetime follows a BBXII distribution. Convincing results are obtained.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70179632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some new criteria for judging $ mathcal{H} $-tensors and their applications","authors":"Wenbin Gong, Yaqiang Wang","doi":"10.3934/math.2023381","DOIUrl":"https://doi.org/10.3934/math.2023381","url":null,"abstract":"$ mathcal{H} $-tensors play a key role in identifying the positive definiteness of even-order real symmetric tensors. Some criteria have been given since it is difficult to judge whether a given tensor is an $ mathcal{H} $-tensor, and their range of judgment has been limited. In this paper, some new criteria, from an increasing constant $ k $ to scale the elements of a given tensor can expand the range of judgment, are obtained. Moreover, as an application of those new criteria, some sufficient conditions for judging positive definiteness of even-order real symmetric tensors are proposed. In addition, some numerical examples are presented to illustrate those new results.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70181534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence and compatibility of positive solutions for boundary value fractional differential equation with modified analytic kernel","authors":"A. Kalsoom, Sehar Afsheen, A. Azam, Faryad Ali","doi":"10.3934/math.2023390","DOIUrl":"https://doi.org/10.3934/math.2023390","url":null,"abstract":"In this article, a Green's function for a fractional boundary value problem in connection with modified analytic kernel has been constructed to study the existence of multiple solutions of a type of characteristic fractional boundary value problems. It is done here by using a well-known result: Krasnoselskii fixed point theorem. Moreover, a practical example is created to understand the importance of main results regarding the existence of solution of a boundary value fractional differential problem with homogeneous conditions. This example analytically and graphically, explains circumstances under which the Green's functions with different types of differential operator are compatible.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70182202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Differential subordination, superordination results associated with Pascal distribution","authors":"K. Saritha, K. Thilagavathi","doi":"10.3934/math.2023395","DOIUrl":"https://doi.org/10.3934/math.2023395","url":null,"abstract":"This paper aims to study differential subordination and superordination preserving properties for certain analytic univalent functions with in the open unit disk. In the present investigation, we obtain some subordination and superordination results involving Pascal distribution series for certain normalized analytic functions in the open unit disk. Also we estimate the sandwich results for the same class.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70182217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Blowup for $ {{rm{C}}}^{1} $ solutions of Euler equations in $ {{rm{R}}}^{N} $ with the second inertia functional of reference","authors":"Manwai Yuen","doi":"10.3934/math.2023412","DOIUrl":"https://doi.org/10.3934/math.2023412","url":null,"abstract":"<abstract><p>The compressible Euler equations are an elementary model in mathematical fluid mechanics. In this article, we combine the Sideris and Makino-Ukai-Kawashima's classical functional techniques to study the new second inertia functional of reference:</p> <p><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ { H}_{ref}{ (t) = }frac{1}{2}int_{Omega(t)}left( { rho-bar{rho}}right) leftvert { vec{x} }rightvert ^{2}dV{{ , }} $end{document} </tex-math></disp-formula></p> <p>for the blowup phenomena of $ C^{1} $ solutions $ (rho, vec{u}) $ with the support of $ left({ rho-bar{rho}}, vec{u}right) $, and with a positive constant $ { bar{rho}} $ for the adiabatic index $ gamma > 1 $. We find that if the total reference mass</p> <p><disp-formula> <label/> <tex-math id=\"FE2\"> begin{document}$ M_{ref}(0) = { int_{{bf R}^{N}}} (rho_{0}({ vec{x}})-bar{rho})dVgeq0, $end{document} </tex-math></disp-formula></p> <p>and the total reference energy</p> <p><disp-formula> <label/> <tex-math id=\"FE3\"> begin{document}$ E_{ref}(0) = int_{{bf R}^{N}}left( frac{1}{2}rho_{0}({ vec {x}})leftvert vec{u}_{0}({ vec{x}})rightvert ^{2}+frac {K}{gamma-1}left( rho_{0}^{gamma}({ vec{x}})-bar{rho }^{gamma}right) right) dV, $end{document} </tex-math></disp-formula></p> <p>with a positive constant $ K $ is sufficiently large, then the corresponding solution blows up on or before any finite time $ T > 0 $.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70182449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability, bifurcation, and chaos control in a discrete predator-prey model with strong Allee effect","authors":"Ali Al Khabyah, Rizwan Ahmed, M. Akram, S. Akhtar","doi":"10.3934/math.2023408","DOIUrl":"https://doi.org/10.3934/math.2023408","url":null,"abstract":"This work considers a discrete-time predator-prey system with a strong Allee effect. The existence and topological classification of the system's possible fixed points are investigated. Furthermore, the existence and direction of period-doubling and Neimark-Sacker bifurcations are explored at the interior fixed point using bifurcation theory and the center manifold theorem. A hybrid control method is used for controlling chaos and bifurcations. Some numerical examples are presented to verify our theoretical findings. Numerical simulations reveal that the discrete model has complex dynamics. Moreover, it is shown that the system with the Allee effect requires a much longer time to reach its interior fixed point.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70182612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"q-Spherical fuzzy rough sets and their usage in multi-attribute decision-making problems","authors":"Ahmad Bin Azim, Ahmad Aloqaily, Asad Ali, Sumbal Ali, Nabil Mlaiki, F. Hussain","doi":"10.3934/math.2023415","DOIUrl":"https://doi.org/10.3934/math.2023415","url":null,"abstract":"This article's purpose is to investigate and generalize the concepts of rough set, in addition to the q-spherical fuzzy set, and to introduce a novel concept that is called q-spherical fuzzy rough set (q-SFRS). This novel approach avoids the complications of more recent ideas like the intuitionistic fuzzy rough set, Pythagorean fuzzy rough set, and q-rung orthopair fuzzy rough set. Since mathematical operations known as \"aggregation operators\" are used to bring together sets of data. Popular aggregation operations include the arithmetic mean and the weighted mean. The key distinction between the weighted mean and the arithmetic mean is that the latter allows us to weight the various values based on their importance. Various aggregation operators make different assumptions about the input (data kinds) and the kind of information that may be included in the model. Because of this, some new q-spherical fuzzy rough weighted arithmetic mean operator and q-spherical fuzzy rough weighted geometric mean operator have been introduced. The developed operators are more general. Because the picture fuzzy rough weighted arithmetic mean (PFRWAM) operator, picture fuzzy rough weighted geometric mean (PFRWGM) operator, spherical fuzzy rough weighted arithmetic mean (SFRWAM) operator and spherical fuzzy rough weighted geometric mean (SFRWGM) operator are all the special cases of the q-SFRWAM and q-SFRWGM operators. When parameter q = 1, the q-SFRWAM operator reduces the PFRWAM operator, and the q-SFRWGM operator reduces the PFRWGM operator. When parameter q = 2, the q-SFRWAM operator reduces the SFRWAM operator, and the q-SFRWGM operator reduces the SFRWGM operator. Besides, our approach is more flexible, and decision-makers can choose different values of parameter q according to the different risk attitudes. In addition, the basic properties of these newly presented operators have been analyzed in great depth and expounded upon. Additionally, a technique called multi-criteria decision-making (MCDM) has been established, and a detailed example has been supplied to back up the recently introduced work. An evaluation of the offered methodology is established at the article's conclusion. The results of this research show that, compared to the q-spherical fuzzy set, our method is better and more effective.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70183173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some results in function weighted b-metric spaces","authors":"B. Nurwahyu, N. Aris, Firman","doi":"10.3934/math.2023417","DOIUrl":"https://doi.org/10.3934/math.2023417","url":null,"abstract":"<abstract> <p>In this paper, we introduce <italic>F</italic>-<italic>b</italic>-metric space (function weighted <italic>b</italic>-metric space) as a generalization of the <italic>F</italic>-metric space (the function weighted metric space). We also propose and prove some topological properties of the <italic>F</italic>-<italic>b</italic>-metric space, the theorems of fixed point and the common fixed point for the generalized expansive mappings, and an application on dynamic programing.</p> </abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70183280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Orbital stability of periodic standing waves of the coupled Klein-Gordon-Zakharov equations","authors":"Qiuying Li, Xiaoxiao Zheng, Zhenguo Wang","doi":"10.3934/math.2023430","DOIUrl":"https://doi.org/10.3934/math.2023430","url":null,"abstract":"This paper investigates the orbital stability of periodic standing waves for the following coupled Klein-Gordon-Zakharov equations begin{document} $ begin{equation*} left{ begin{aligned} &u_{tt}-u_{xx}+u+alpha uv+beta|u|^{2}u = 0, &v_{tt}-v_{xx} = (|u|^{2})_{xx}, end{aligned} right. end{equation*} $ end{document} where $alpha>0$ and $beta$ are two real numbers and $alpha>beta$. Under some suitable conditions, we show the existence of a smooth curve positive standing wave solutions of dnoidal type with a fixed fundamental period L for the above equations. Further, we obtain the stability of the dnoidal waves for the coupled Klein-Gordon-Zakharov equations by applying the abstract stability theory and combining the detailed spectral analysis given by using Lam'{e} equation and Floquet theory. When period $Lrightarrowinfty$, dnoidal type will turn into sech-type in the sense of limit. In such case, we can obtain stability of sech-type standing waves. In particular, $beta = 0$ is advisable, we still can show the the stability of the dnoidal type and sech-type standing waves for the classical Klein-Gordon-Zakharov equations.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70183834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}