Abstract In this article, we will prove the existence of infinitely many solutions for a class of quasilinear Schrödinger equations without assuming the 4-superlinear at infinity on the nonlinearity. We achieve our goal by using the Fountain theorem.
{"title":"Infinitely many solutions for quasilinear Schrödinger equations with sign-changing nonlinearity without the aid of 4-superlinear at infinity","authors":"M. Khiddi, L. Essafi","doi":"10.1515/dema-2022-0169","DOIUrl":"https://doi.org/10.1515/dema-2022-0169","url":null,"abstract":"Abstract In this article, we will prove the existence of infinitely many solutions for a class of quasilinear Schrödinger equations without assuming the 4-superlinear at infinity on the nonlinearity. We achieve our goal by using the Fountain theorem.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"831 - 842"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42693140","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}
Abstract A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions. An extensive bibliography is also provided.
{"title":"Some recent results on singular p-Laplacian equations","authors":"U. Guarnotta, R. Livrea, S. Marano","doi":"10.1515/dema-2022-0031","DOIUrl":"https://doi.org/10.1515/dema-2022-0031","url":null,"abstract":"Abstract A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions. An extensive bibliography is also provided.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"416 - 428"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44317369","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}
Nour El-Houda Bezzar, L. Laimeche, A. Meraoumia, L. Houam
Abstract Recently, electricity consumption forecasting has attracted much research due to its importance in our daily life as well as in economic activities. This process is seen as one of the ways to manage future electricity needs, including anticipating the supply-demand balance, especially at peak times, and helping the customer make real-time decisions about their consumption. Therefore, based on statistical techniques (ST) and/or artificial intelligence (AI), many forecasting models have been developed in the literature, but unfortunately, in addition to poor choice of the appropriate model, time series datasets were used directly without being seriously analyzed. In this article, we have proposed an efficient electricity consumption prediction model that takes into account the shortcomings mentioned earlier. Therefore, the database was analyzed to address all anomalies such as non-numeric values, aberrant, and missing values. In addition, by analyzing the correlation between the data, the possible periods for forecasting electricity consumption were determined. The experimental results carried out on the Individual Household Electricity Power Consumption dataset showed a clear superiority of the proposed model over most of the ST and/or AI-based models proposed in the literature.
{"title":"Data analysis-based time series forecast for managing household electricity consumption","authors":"Nour El-Houda Bezzar, L. Laimeche, A. Meraoumia, L. Houam","doi":"10.1515/dema-2022-0176","DOIUrl":"https://doi.org/10.1515/dema-2022-0176","url":null,"abstract":"Abstract Recently, electricity consumption forecasting has attracted much research due to its importance in our daily life as well as in economic activities. This process is seen as one of the ways to manage future electricity needs, including anticipating the supply-demand balance, especially at peak times, and helping the customer make real-time decisions about their consumption. Therefore, based on statistical techniques (ST) and/or artificial intelligence (AI), many forecasting models have been developed in the literature, but unfortunately, in addition to poor choice of the appropriate model, time series datasets were used directly without being seriously analyzed. In this article, we have proposed an efficient electricity consumption prediction model that takes into account the shortcomings mentioned earlier. Therefore, the database was analyzed to address all anomalies such as non-numeric values, aberrant, and missing values. In addition, by analyzing the correlation between the data, the possible periods for forecasting electricity consumption were determined. The experimental results carried out on the Individual Household Electricity Power Consumption dataset showed a clear superiority of the proposed model over most of the ST and/or AI-based models proposed in the literature.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"900 - 921"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46336428","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}
Abstract The pointwise estimates of the deviation T n , A f ( ⋅ ) − f ( ⋅ ) {T}_{n,A}f(cdot )-fleft(cdot ) in terms of pointwise moduli of continuity based on the points of differentiability of indefinite integral of f f , with application of the rth differences of the entries of A A , are proved. The similar results in case of the Lebesgue points are considered, too. Analogical results on norm approximation with remarks and corollaries are also given.
{"title":"Approximation of integrable functions by general linear matrix operators of their Fourier series","authors":"V. Mishra, W. Łenski, B. Szal","doi":"10.1515/dema-2022-0009","DOIUrl":"https://doi.org/10.1515/dema-2022-0009","url":null,"abstract":"Abstract The pointwise estimates of the deviation T n , A f ( ⋅ ) − f ( ⋅ ) {T}_{n,A}f(cdot )-fleft(cdot ) in terms of pointwise moduli of continuity based on the points of differentiability of indefinite integral of f f , with application of the rth differences of the entries of A A , are proved. The similar results in case of the Lebesgue points are considered, too. Analogical results on norm approximation with remarks and corollaries are also given.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"136 - 152"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49636939","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}
Abstract The bank run phenomenon, mostly due to rumor spread about the financial health of given financial institutions, is prejudicious to the stability of financial systems. In this paper, by using the epidemiological approach, we propose a nonlinear model for describing the impact of rumor on the banking crisis spread. We establish conditions under which the crisis dies out or remains permanent. We also solve an optimal control problem focusing on the minimization, at the lowest cost, of the number of stressed banks, as well as the number of banks undergoing the restructuring process. Numerical simulations are performed to illustrate theoretical results obtained.
{"title":"Mathematical modeling and optimal control of the impact of rumors on the banking crisis","authors":"C. Tadmon, Eric Rostand Njike-Tchaptchet","doi":"10.1515/dema-2022-0007","DOIUrl":"https://doi.org/10.1515/dema-2022-0007","url":null,"abstract":"Abstract The bank run phenomenon, mostly due to rumor spread about the financial health of given financial institutions, is prejudicious to the stability of financial systems. In this paper, by using the epidemiological approach, we propose a nonlinear model for describing the impact of rumor on the banking crisis spread. We establish conditions under which the crisis dies out or remains permanent. We also solve an optimal control problem focusing on the minimization, at the lowest cost, of the number of stressed banks, as well as the number of banks undergoing the restructuring process. Numerical simulations are performed to illustrate theoretical results obtained.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"90 - 118"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43490523","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}
Abstract The aim of this article is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential functions on Z p {{mathbb{Z}}}_{p} . We find some explicit expressions for the fully degenerate Bernoulli polynomials and numbers in terms of the degenerate Stirling numbers of the second kind, the degenerate r r -Stirling numbers of the second kind, and the degenerate Stirling polynomials. We also consider the degenerate poly-Bernoulli polynomials and derive explicit representations for them in terms of the same degenerate Stirling numbers and polynomials.
{"title":"Fully degenerate Bernoulli numbers and polynomials","authors":"Taekyun Kim, Dae San Kim, Jin-Woo Park","doi":"10.1515/dema-2022-0160","DOIUrl":"https://doi.org/10.1515/dema-2022-0160","url":null,"abstract":"Abstract The aim of this article is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential functions on Z p {{mathbb{Z}}}_{p} . We find some explicit expressions for the fully degenerate Bernoulli polynomials and numbers in terms of the degenerate Stirling numbers of the second kind, the degenerate r r -Stirling numbers of the second kind, and the degenerate Stirling polynomials. We also consider the degenerate poly-Bernoulli polynomials and derive explicit representations for them in terms of the same degenerate Stirling numbers and polynomials.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"604 - 614"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44954720","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}
Abstract Quite recently, a new minimal structure m H ⋆ {m}_{H}^{star } and an m n mn - ℋ g {{mathcal{ {mathcal H} }}}_{g} -closed set have been introduced in a previous study [T. Noiri and V. Popa, Closed sets in hereditary bi m-spaces, Questions Answers General Topol. 38 (2020), 133–142] by using two minimal structures m, n n and a hereditary class ℋ {mathcal{ {mathcal H} }} . In this paper, we introduce and investigate the notions of ( m , n ) left(m,n) - ℋ g ⋆ {{mathcal{ {mathcal H} }}}_{g}^{star } -regularity and ( m , n ) left(m,n) - ℋ g ⋆ {{mathcal{ {mathcal H} }}}_{g}^{star } -normality in a hereditary bi m-space ( X , m , n , ℋ ) left(X,m,n,{mathcal{ {mathcal H} }}) .
摘要最近，一个新的极小结构mH⋆{m}_{H} ^｛star｝和一个ℋ 在先前的研究[T.Noiri和V.Popa，遗传双m-空间中的闭集，问答通用拓扑.38（2020），133–142]中，通过使用两个极小结构m，n n和一个遗传类引入了g｛mathcal｛｛math cal H｝｝}_｛g｝-闭集ℋ ｛mathcal｝｝。在本文中，我们引入并研究了（m，n）left（m，n）-ℋ g⋆｛mathcal｛math H｝｝｝_｛g｝^｛star｝-正则性和（m，n）left（m，n）-ℋ 遗传双m空间（X，m，n，ℋ ) left（X，m，n，｛mathcal｛｛math cal H｝｝）。
{"title":"Regularity and normality in hereditary bi m-spaces","authors":"A. Al-Omari, S. Al Ghour, T. Noiri","doi":"10.1515/dema-2022-0021","DOIUrl":"https://doi.org/10.1515/dema-2022-0021","url":null,"abstract":"Abstract Quite recently, a new minimal structure m H ⋆ {m}_{H}^{star } and an m n mn - ℋ g {{mathcal{ {mathcal H} }}}_{g} -closed set have been introduced in a previous study [T. Noiri and V. Popa, Closed sets in hereditary bi m-spaces, Questions Answers General Topol. 38 (2020), 133–142] by using two minimal structures m, n n and a hereditary class ℋ {mathcal{ {mathcal H} }} . In this paper, we introduce and investigate the notions of ( m , n ) left(m,n) - ℋ g ⋆ {{mathcal{ {mathcal H} }}}_{g}^{star } -regularity and ( m , n ) left(m,n) - ℋ g ⋆ {{mathcal{ {mathcal H} }}}_{g}^{star } -normality in a hereditary bi m-space ( X , m , n , ℋ ) left(X,m,n,{mathcal{ {mathcal H} }}) .","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"226 - 237"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46704812","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}
Abstract By using the theory of fixed point index and spectral theory of linear operators, we study the existence of positive solutions for Riemann-Liouville fractional differential equations at resonance. Our approach will provide some new ideas for the study of this kind of problem.
{"title":"Positive solutions for fractional differential equation at resonance under integral boundary conditions","authors":"Youyu Wang, Yue Huang, Xianfei Li","doi":"10.1515/dema-2022-0026","DOIUrl":"https://doi.org/10.1515/dema-2022-0026","url":null,"abstract":"Abstract By using the theory of fixed point index and spectral theory of linear operators, we study the existence of positive solutions for Riemann-Liouville fractional differential equations at resonance. Our approach will provide some new ideas for the study of this kind of problem.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"238 - 253"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42391098","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}
Manar A. Alqudah, C. Garodia, I. Uddin, Juan J. Nieto
Abstract The motive of this article is to study a modified iteration scheme for monotone nonexpansive mappings in the class of uniformly convex Banach space and establish some convergence results. We obtain weak and strong convergence results. In addition, we present a nontrivial numerical example to show the convergence of our iteration scheme. To demonstrate the utility of our scheme, we discuss the solution of nonlinear integral equations as an application, which is again supported by a nontrivial example.
{"title":"Computation of solution of integral equations via fixed point results","authors":"Manar A. Alqudah, C. Garodia, I. Uddin, Juan J. Nieto","doi":"10.1515/dema-2022-0172","DOIUrl":"https://doi.org/10.1515/dema-2022-0172","url":null,"abstract":"Abstract The motive of this article is to study a modified iteration scheme for monotone nonexpansive mappings in the class of uniformly convex Banach space and establish some convergence results. We obtain weak and strong convergence results. In addition, we present a nontrivial numerical example to show the convergence of our iteration scheme. To demonstrate the utility of our scheme, we discuss the solution of nonlinear integral equations as an application, which is again supported by a nontrivial example.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"772 - 785"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41922803","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}
Abstract We establish an accurate and efficient scheme with four-order accuracy for solving three-dimensional (3D) acoustic wave equation. First, the local one-dimensional method is used to transfer the 3D wave equation into three one-dimensional wave equations. Then, a new scheme is obtained by the Padé formulas for computation of spatial second derivatives and the correction of the truncation error remainder for discretization of temporal second derivative. It is compact and can be solved directly by the Thomas algorithm. Subsequently, the Fourier analysis method and the Lax equivalence theorem are employed to prove the stability and convergence of the present scheme, which shows that it is conditionally stable and convergent, and the stability condition is superior to that of most existing numerical methods of equivalent order of accuracy in the literature. It allows us to reduce computational cost with relatively large time step lengths. Finally, numerical examples have demonstrated high accuracy, stability, and efficiency of our method.
{"title":"An accurate and efficient local one-dimensional method for the 3D acoustic wave equation","authors":"Mengling Wu, Yunzhi Jiang, Y. Ge","doi":"10.1515/dema-2022-0148","DOIUrl":"https://doi.org/10.1515/dema-2022-0148","url":null,"abstract":"Abstract We establish an accurate and efficient scheme with four-order accuracy for solving three-dimensional (3D) acoustic wave equation. First, the local one-dimensional method is used to transfer the 3D wave equation into three one-dimensional wave equations. Then, a new scheme is obtained by the Padé formulas for computation of spatial second derivatives and the correction of the truncation error remainder for discretization of temporal second derivative. It is compact and can be solved directly by the Thomas algorithm. Subsequently, the Fourier analysis method and the Lax equivalence theorem are employed to prove the stability and convergence of the present scheme, which shows that it is conditionally stable and convergent, and the stability condition is superior to that of most existing numerical methods of equivalent order of accuracy in the literature. It allows us to reduce computational cost with relatively large time step lengths. Finally, numerical examples have demonstrated high accuracy, stability, and efficiency of our method.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"55 1","pages":"528 - 552"},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47239119","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：