TY - JOUR AU - Tarcsay, Zsigmond AU - Sebestyén, Zoltán TI - Reduction of positive self-adjoint extensions JF - OPUSCULA MATHEMATICA J2 - OPUSC MATHEMATICA VL - 44 PY - 2024 IS - 3 SP - 425 EP - 438 PG - 14 SN - 1232-9274 DO - 10.7494/OpMath.2024.44.3.425 UR - https://m2.mtmt.hu/api/publication/34751048 ID - 34751048 N1 - Zsigmond Tarcsay was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP–22-5-ELTE-1096 New National Excellence Program of the Ministry for Innovation and Technology. LA - English DB - MTMT ER - TY - JOUR AU - El-Matary, Bassant M. AU - El-Morshedy, Hassan A. AU - Benekas, Vasileios AU - Stavroulakis, Ioannis P. TI - Oscillation conditions for difference equations with several variable delays JF - OPUSCULA MATHEMATICA J2 - OPUSC MATHEMATICA VL - 43 PY - 2023 IS - 6 SP - 789 EP - 801 PG - 13 SN - 1232-9274 DO - 10.7494/OpMath.2023.43.6.789 UR - https://m2.mtmt.hu/api/publication/34082427 ID - 34082427 AB - A technique is developed to establish a new oscillation criterion for a first-order linear difference equation with several delays and non-negative coefficients. Our result improves recent oscillation criteria and covers the cases of monotone and non-monotone delays. Moreover, the paper is concluded with an illustrative example to show the applicability and strength of our result. LA - English DB - MTMT ER - TY - JOUR AU - Tavares, Leandro S. AU - Sousa, J. Vanterler C. TI - SOLUTIONS FOR A NONHOMOGENEOUS p&q-LAPLACIAN PROBLEM VIA VARIATIONAL METHODS AND SUB-SUPERSOLUTION TECHNIQUE JF - OPUSCULA MATHEMATICA J2 - OPUSC MATHEMATICA VL - 43 PY - 2023 IS - 4 SP - 603 EP - 613 PG - 11 SN - 1232-9274 DO - 10.7494/OpMath.2023.43.4.603 UR - https://m2.mtmt.hu/api/publication/34349785 ID - 34349785 AB - In this paper it is obtained, through variational methods and sub-supersolution arguments, existence and multiplicity of solutions for a nonhomogeneous problem which arise in several branches of science such as chemical reactions, biophysics and plasma physics. Under a general hypothesis it is proved an existence result and multiple solutions are obtained by considering an additional natural condition. LA - English DB - MTMT ER - TY - JOUR AU - Fechner, Zywilla AU - Gselmann, Eszter AU - Székelyhidi, László TI - Generalized derivations and generalized exponential monomials on hypergroups JF - OPUSCULA MATHEMATICA J2 - OPUSC MATHEMATICA VL - 43 PY - 2023 IS - 4 SP - 493 EP - 505 PG - 13 SN - 1232-9274 DO - 10.7494/OpMath.2023.43.4.493 UR - https://m2.mtmt.hu/api/publication/34087010 ID - 34087010 AB - In one of our former papers "Endomorphisms of the measure algebra of commutative hypergroups" we considered exponential monomials on hypergroups and higher order derivations of the corresponding measure algebra. Continuing with this, we are now looking for the connection between the generalized exponential polynomials of a commutative hypergroup and the higher order derivations of the corresponding measure algebra. LA - English DB - MTMT ER - TY - JOUR AU - Kennedy, Benjamin B. TI - Periodic, nonperiodic, and chaotic solutions for a class of difference equations with negative feedback JF - OPUSCULA MATHEMATICA J2 - OPUSC MATHEMATICA VL - 43 PY - 2023 IS - 4 SP - 507 EP - 546 PG - 40 SN - 1232-9274 DO - 10.7494/OpMath.2023.43.4.507 UR - https://m2.mtmt.hu/api/publication/34015297 ID - 34015297 AB - We study the scalar difference equation \[x(k+1) = x(k) + \frac{f(x(k-N))}{N},\] where \(f\) is nonincreasing with negative feedback. This equation is a discretization of the well-studied differential delay equation \[x'(t) = f(x(t-1)).\] We examine explicit families of such equations for which we can find, for infinitely many values of $ and appropriate parameter values, various dynamical behaviors including periodic solutions with large numbers of sign changes per minimal period, solutions that do not converge to periodic solutions, and chaos. We contrast these behaviors with the dynamics of the limiting differential equation. Our primary tool is the analysis of return maps for the difference equations that are conjugate to continuous self-maps of the circle. LA - English DB - MTMT ER - TY - JOUR AU - Godoy, Tomas TI - SINGULAR ELLIPTIC PROBLEMS WITH DIRICHLET OR MIXED DIRICHLET-NEUMANN NON-HOMOGENEOUS BOUNDARY CONDITIONS JF - OPUSCULA MATHEMATICA J2 - OPUSC MATHEMATICA VL - 43 PY - 2023 IS - 1 SP - 19 EP - 46 PG - 28 SN - 1232-9274 DO - 10.7494/OpMath.2023.43.1.19 UR - https://m2.mtmt.hu/api/publication/33943060 ID - 33943060 AB - Let Omega be a C-2 bounded domain in R-n such that partial derivative Omega = Gamma(1) boolean OR Gamma(2), where Gamma(1) and Gamma(2) are disjoint closed subsets of partial derivative Omega, and consider the problem -Delta u = g(. , u) in Omega, u = tau on Gamma(1), partial derivative u/partial derivative nu = eta on Gamma(2), where 0 <= t is an element of W-1/2,W-2(Gamma(1)), eta is an element of (H-0,Gamma 1(1), (Omega))', and g : Omega x(0,infinity) -> R is a nonnegative Caratheodory function. Under suitable assumptions on g and eta we prove the existence and uniqueness of a positive weak solution of this problem. Our assumptions allow g to be singular at s = 0 and also at x is an element of S for some suitable subsets S subset of (Omega) over bar. The Dirichlet problem -Delta u = g(., u) in Omega, u = sigma on partial derivative Omega is also studied in the case when 0 <= sigma is an element of W-1/2,W-2 (Omega). LA - English DB - MTMT ER - TY - JOUR AU - Bouhadjera, Feriel AU - Said, Elias Ould TI - STRONG CONSISTENCY OF THE LOCAL LINEAR RELATIVE REGRESSION ESTIMATOR FOR CENSORED DATA JF - OPUSCULA MATHEMATICA J2 - OPUSC MATHEMATICA VL - 42 PY - 2022 IS - 6 SP - 805 EP - 832 PG - 28 SN - 1232-9274 DO - 10.7494/OpMath.2022.42.6.805 UR - https://m2.mtmt.hu/api/publication/33840469 ID - 33840469 AB - In this paper, we combine the local linear approach to the relative error regression estimation method to build a new estimator of the regression operator when the response variable is subject to random right censoring. We establish the uniform almost sure consistency with rate over a compact set of the proposed estimator. Numerical studies, firstly on simulated data, then on a real data set concerning the death times of kidney transplant patients, were conducted. These practical studies clearly show the superiority of the new estimator compared to competitive estimators. LA - English DB - MTMT ER - TY - JOUR AU - Hata, Yuki AU - Matsunaga, Hideaki TI - STABILITY SWITCHES IN A LINEAR DIFFERENTIAL EQUATION WITH TWO DELAYS JF - OPUSCULA MATHEMATICA J2 - OPUSC MATHEMATICA VL - 42 PY - 2022 IS - 5 SP - 673 EP - 690 PG - 18 SN - 1232-9274 DO - 10.7494/OpMath.2022.42.5.673 UR - https://m2.mtmt.hu/api/publication/34585306 ID - 34585306 N1 - Funding Agency and Grant Number: JSPS KAKENHI [JP19K03524] Funding text: This research of the second author is supported in part by JSPS KAKENHI Grants-in-Aid for Scientific Research (C) Grant Number JP19K03524. AB - This paper is devoted to the study of the effect of delays on the asymptotic stability of a linear differential equation with two delays x'(t) = -ax(t) - bx(t - tau) - cx(t - 2 tau), t >= 0, where a, b, and c are real numbers and tau > 0. We establish some explicit conditions for the zero solution of the equation to be asymptotically stable. As a corollary, it is shown that the zero solution becomes unstable eventually after undergoing stability switches finite times when tau increases only if c - a < 0 and root-8c(c - a) < vertical bar b vertical bar < a+ c. The explicit stability dependence on the changing t is also described. LA - English DB - MTMT ER - TY - JOUR AU - Dzurina, Jozef TI - PROPERTIES OF EVEN ORDER LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS OF MIXED TYPE JF - OPUSCULA MATHEMATICA J2 - OPUSC MATHEMATICA VL - 42 PY - 2022 IS - 5 SP - 659 EP - 671 PG - 13 SN - 1232-9274 DO - 10.7494/OpMath.2022.42.5.659 UR - https://m2.mtmt.hu/api/publication/33450866 ID - 33450866 AB - This paper is concerned with oscillatory behavior of linear functional differential equations of the typey((n))(t) = p(t)y(tau(t))with mixed deviating arguments which means that its both delayed and advanced parts are unbounded subset of (0, infinity). Our attention is oriented to the Euler type of equation, i.e. when p(t) similar to a/t(n). LA - English DB - MTMT ER - TY - JOUR AU - Baculikova, Blanka TI - OSCILLATION OF EVEN ORDER LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH MIXED DEVIATING ARGUMENTS JF - OPUSCULA MATHEMATICA J2 - OPUSC MATHEMATICA VL - 42 PY - 2022 IS - 4 SP - 549 EP - 560 PG - 12 SN - 1232-9274 DO - 10.7494/OpMath.2022.42.4.549 UR - https://m2.mtmt.hu/api/publication/33450868 ID - 33450868 AB - In the paper, we study oscillation and asymptotic properties for even order linear functional differential equationsy((n))(t) = p(t)y(tau(t))with mixed deviating arguments, i.e. when both delayed and advanced parts of tau(t) are significant. The presented results essentially improve existing ones. LA - English DB - MTMT ER -