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Nonlinear Katugampola Fractional Differential Equation with Mixed Boundary Conditions 具有混合边界条件的非线性Katugampola分数阶微分方程
Tatra Mountains Mathematical Publications Pub Date : 2023-06-01 DOI: 10.2478/tmmp-2023-0013
Barbara Lupińska
{"title":"Nonlinear Katugampola Fractional Differential Equation with Mixed Boundary Conditions","authors":"Barbara Lupińska","doi":"10.2478/tmmp-2023-0013","DOIUrl":"https://doi.org/10.2478/tmmp-2023-0013","url":null,"abstract":"Abstract This paper discusses the existence and uniqueness of solutions for a class of nonlinear fractional differential equations with a mixed fractional boundary value using Banach and Schaefer fixed-point theorems. The examples illustrating the main results are given.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"84 1","pages":"25 - 34"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46362789","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
Existence, Uniqueness and Ulam-Hyers-Rassias Stability of Differential Coupled Systems with Riesz-Caputo Fractional Derivative 具有Riesz-Caputo分数阶导数的微分耦合系统的存在唯一性及Ulam-Hyers-Rassias稳定性
Tatra Mountains Mathematical Publications Pub Date : 2023-06-01 DOI: 10.2478/tmmp-2023-0019
Abdelkrim Salim, J. Lazreg, M. Benchohra
{"title":"Existence, Uniqueness and Ulam-Hyers-Rassias Stability of Differential Coupled Systems with Riesz-Caputo Fractional Derivative","authors":"Abdelkrim Salim, J. Lazreg, M. Benchohra","doi":"10.2478/tmmp-2023-0019","DOIUrl":"https://doi.org/10.2478/tmmp-2023-0019","url":null,"abstract":"Abstract This article deals with the existence, uniqueness and Ulam-Hyers--Rassias stability results for a class of coupled systems for implicit fractional differential equations with Riesz-Caputo fractional derivative and boundary conditions. We will employ the Banach’s contraction principle as well as Schauder’s fixed point theorem to demonstrate our existence results. We provide an example to illustrate the obtained results.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"84 1","pages":"111 - 138"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46317719","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
Exponential Stability of Integro-Differential Volterra Equation on Time Scales 积分微分Volterra方程在时间尺度上的指数稳定性
Tatra Mountains Mathematical Publications Pub Date : 2023-06-01 DOI: 10.2478/tmmp-2023-0017
U. Ostaszewska, E. Schmeidel, M. Zdanowicz
{"title":"Exponential Stability of Integro-Differential Volterra Equation on Time Scales","authors":"U. Ostaszewska, E. Schmeidel, M. Zdanowicz","doi":"10.2478/tmmp-2023-0017","DOIUrl":"https://doi.org/10.2478/tmmp-2023-0017","url":null,"abstract":"Abstract We study the Volterra integro-differential equation on time scales and provide sufficient conditions for boundness of all solutions of considered equation. Using that result, we present the conditions for exponential stability of considered equation. All the results proved on the general time scale include results for both integral and discrete Volterra equations.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"84 1","pages":"77 - 86"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41362994","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
Nonautonomous Fold Bifurcations from Spectral Intervals of Higher Strict Multiplicity 高严格多重谱区间的非自治折叠分岔
Tatra Mountains Mathematical Publications Pub Date : 2023-06-01 DOI: 10.2478/tmmp-2023-0018
C. Pötzsche
{"title":"Nonautonomous Fold Bifurcations from Spectral Intervals of Higher Strict Multiplicity","authors":"C. Pötzsche","doi":"10.2478/tmmp-2023-0018","DOIUrl":"https://doi.org/10.2478/tmmp-2023-0018","url":null,"abstract":"Abstract We provide two sufficient criteria for the bifurcation of bounded entire or homoclinic solutions to nonautonomous difference equations depending on a single real parameter. Our analysis is based on a nonhyperbolic solution, whose variational equation possesses exponential dichotomies on semiaxes ensuring that the corresponding critical spectral interval of the dichotomy spectrum has strict multiplicity > 1. This extends earlier results on the fold bifurcation.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"84 1","pages":"87 - 110"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44553569","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
Asymptotic Properties of Solutions to Discrete Sturm-Liouville Monotone Type Equations 离散Sturm-Liouville单调型方程解的渐近性质
Tatra Mountains Mathematical Publications Pub Date : 2023-06-01 DOI: 10.2478/tmmp-2023-0014
Janusz Migda, E. Schmeidel
{"title":"Asymptotic Properties of Solutions to Discrete Sturm-Liouville Monotone Type Equations","authors":"Janusz Migda, E. Schmeidel","doi":"10.2478/tmmp-2023-0014","DOIUrl":"https://doi.org/10.2478/tmmp-2023-0014","url":null,"abstract":"Abstract We investigate the discrete equations of the form Δ(rnΔxn)=anf(xσ(n))+bn. Delta left( {{r_n}Delta {x_n}} right) = {a_n}fleft( {{x_{sigma left( n right)}}} right) + {b_n}. Using the Knaster-Tarski fixed point theorem, we study solutions with prescribed asymptotic behaviour. Our technique allows us to control the degree of approximation. In particular, we present the results concerning harmonic and geometric approximations of solutions.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"84 1","pages":"35 - 44"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48803205","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
Discrete Polylogarithm Functions 离散多对数函数
Tatra Mountains Mathematical Publications Pub Date : 2023-06-01 DOI: 10.2478/tmmp-2023-0012
Tom Cuchta, Dallas D. Freeman
{"title":"Discrete Polylogarithm Functions","authors":"Tom Cuchta, Dallas D. Freeman","doi":"10.2478/tmmp-2023-0012","DOIUrl":"https://doi.org/10.2478/tmmp-2023-0012","url":null,"abstract":"Abstract We investigate a discrete analogue of the polylogarithm function. Difference and summation relations are obtained, as well as its connection to the discrete hypergeometric series.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"84 1","pages":"19 - 24"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44898698","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
Asymptotic Properties of Solutions to Fourth-Order Difference Equations on Time Scales 时间尺度上四阶差分方程解的渐近性质
Tatra Mountains Mathematical Publications Pub Date : 2023-06-01 DOI: 10.2478/tmmp-2023-0016
U. Ostaszewska, E. Schmeidel, M. Zdanowicz
{"title":"Asymptotic Properties of Solutions to Fourth-Order Difference Equations on Time Scales","authors":"U. Ostaszewska, E. Schmeidel, M. Zdanowicz","doi":"10.2478/tmmp-2023-0016","DOIUrl":"https://doi.org/10.2478/tmmp-2023-0016","url":null,"abstract":"Abstract We provide sufficient criteria for the existence of solutions for fourth-order nonlinear dynamic equations on time scales (a(t)xΔ2(t))Δ2=b(t)f(x(t))+c(t), {left( {aleft( t right){x^{{Delta ^2}}}left( t right)} right)^{{Delta ^2}}} = bleft( t right)fleft( {xleft( t right)} right) + cleft( t right), such that for a given function y : 𝕋 → ℝ there exists a solution x : 𝕋 → ℝ to considered equation with asymptotic behaviour x(t)=y(t)+o(1tβ) xleft( t right) = yleft( t right) + oleft( {{1 over {{t^beta }}}} right) . The presented result is applied to the study of solutions to the classical Euler–Bernoulli beam equation, which means that it covers the case 𝕋 = ℝ.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"84 1","pages":"61 - 76"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68923074","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
Modifications of the Samuelson Economic Cycle Model 萨缪尔森经济周期模型的修正
Tatra Mountains Mathematical Publications Pub Date : 2023-06-01 DOI: 10.2478/tmmp-2023-0015
Paulina Naumowicz, M. Ruzicková
{"title":"Modifications of the Samuelson Economic Cycle Model","authors":"Paulina Naumowicz, M. Ruzicková","doi":"10.2478/tmmp-2023-0015","DOIUrl":"https://doi.org/10.2478/tmmp-2023-0015","url":null,"abstract":"Abstract The paper presents an analysis of modifications of the standard discrete Samuelson model with determination of the stability of the equilibrium point. The stability region of the equilibrium point depending on the parameters contained in each model is determined using the Schur-Cohn stability criterion.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"84 1","pages":"45 - 60"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44903507","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
Uniqueness for an Inverse Quantum-Dirac Problem with Given Weyl Function 给定Weyl函数的逆量子-狄拉克问题的唯一性
Tatra Mountains Mathematical Publications Pub Date : 2023-06-01 DOI: 10.2478/tmmp-2023-0011
M. Bohner, Ayça Çetinkaya
{"title":"Uniqueness for an Inverse Quantum-Dirac Problem with Given Weyl Function","authors":"M. Bohner, Ayça Çetinkaya","doi":"10.2478/tmmp-2023-0011","DOIUrl":"https://doi.org/10.2478/tmmp-2023-0011","url":null,"abstract":"Abstract In this work, we consider a boundary value problem for a q-Dirac equation. We prove orthogonality of the eigenfunctions, realness of the eigenvalues, and we study asymptotic formulas of the eigenfunctions. We show that the eigenfunctions form a complete system, we obtain the expansion formula with respect to the eigenfunctions, and we derive Parseval’s equality. We construct the Weyl solution and the Weyl function. We prove a uniqueness theorem for the solution of the inverse problem with respect to the Weyl function.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"84 1","pages":"1 - 18"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48085155","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
Commutativity Theorems and Projection on the Center of a Banach Algebra Banach代数中心上的交换性定理和投影
Tatra Mountains Mathematical Publications Pub Date : 2023-02-01 DOI: 10.2478/tmmp-2023-0009
Mohamed Moumen, L. Taoufiq
{"title":"Commutativity Theorems and Projection on the Center of a Banach Algebra","authors":"Mohamed Moumen, L. Taoufiq","doi":"10.2478/tmmp-2023-0009","DOIUrl":"https://doi.org/10.2478/tmmp-2023-0009","url":null,"abstract":"Abstract Let 𝑥 be a Banach algebra. In this article, on the one hand, we proved some results concerning the continuous projection from 𝑥 to its center. On the other hand, we investigate the commutativity of 𝑥 under specific conditions. Finally, we included some examples and applications to prove that various restrictions in the hypotheses of our theorems are necessary.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"83 1","pages":"119 - 130"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46650553","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
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