József Detki – Key Figure In The Education Of Mathematics At The Civil Engineering Subotica
DOI:
https://doi.org/10.18485/uns_evkonyv.2022.11Keywords:
József Detki, Ph.D. in mathematical science, second-order nonlinear differential equationsAbstract
József Detki was the first teacher of Mathematics at the Faculty of Civil Engineering Subotica with a Ph.D. degree. He was a crucial figure in the establishment of the education of mathematics at the Faculty. He played a significant role in the development of the tradition of teaching at the Faculty in Hungarian language. In this work, we summarize his scientific work on the topic of second-order nonlinear differential equations.
References
Atkinson F. V. (1955): On second-order non-linear oscillations. Pacific J. Math. 5, 643-647.
Bellman R. E. (1943): The stability of solutions of linear differential equations. Duke Math. J. 10, 643-647.
Bellman R. E. (1953): Stability theory of differential equations. New York - Toronto - London: McGraw-Hill Book Co.
Bihari I. (1961): On the nonlinear equation $u»+a(t)u+q(t)f(u^2)=0$. Magyar Tud. Akad. Mat. Kutató Int. Közl. 6, 287-291.
Burton T. A., Grimmer R. C. (1970): Stability properties of $(r(t)u’)’+a(t)f(u)g(u’)=0$. Monatsh. Math. 74, 211-222.
Demidovich B. P. (1951): On stability in the sense of Lyapunov of a linear system of ordinary differential equations. Mat. Sbornik N. S. 28(70), 659-684.
Eliás J. (1979): On the solutions of $n$th order differential equation in $Lsp{2}(0,infty)$. Qualitative theory of differential equations, Vol. I,II (Szeged), 181-191.
Graef J. R., Spikes P. W. (1975): Asymptotic behavior of solutions of a second order nonlinear differential equation. J. Differential Equations 17, 461-476.
Hartman P. (1952): On non-oscillatory linear differential equations of second order. Amer. J. Math. 74, 389-400.
Kamenev I. V. (1969): Oscillation of solutions of second order nonlinear equations, Mat. Zametki 5, 125-136.
Kamenev I. V. (1970a): A certain test for the oscillation of the solutions of a second order ordinary differential equation. (Russian), Mat. Zametki 8, 773-776.
Kamenev I. V. (1970b): The oscillatoriness of the solutions of a second order nonlinear equation with a sign-variable coefficient. (Russian) Differencial’nye Uravnenija 8(6), 1718-1721
Kamenev I. V. (1971): Certain specifically nonlinear oscillation theorems. (Russian), Mat. Zametki 10, 129-134.
Kamenev I. V. (1973): A certain specific nonlinear oscillation theorem. (Russian) Differencial’nye Uravnenija 9, 574-576.
Kamenev I. V. (1977): On the question of the oscillation of the solutions of a second order differential equation with an «integrally small» coefficient. (Russian) Differencial’nye Uravnenija 13, 2141-2148.
Kiguradze I. T. (1962): The capability of certain solutions of ordinary differential equations to oscillate. (Russian) Dokl. Akad. Nauk SSSR 144, 33-36
Myshkis A. D. (1972): Linear differential equations with retarded argument. (Russian) Moscow: Izdat. «Nauka», 352 pp.
Mustafa O. G., Rogovchenko Y. V. (2004a): Limit-point type solutions of nonlinear differential equations. J. Math. Anal. Appl. 294, 548-559.
Mustafa O. G., Rogovchenko Y. V. (2004b): Limit-point criteria for superlinear differential equations. Bull. Belg. Math. Soc. 11, 431-440.
Onose H. (1970): Oscillation theorems for nonlinear second order differential equations. Proc. Amer. Math. Soc. 26, 461-464.
Opial Z. (1959): Nouvelles remarques sur l’équation différentielle $u»+a(t)u=0$. (French) Ann. Polon. Math. 6, 75-81.
Pešić M., Rogovchenko Y. V. (2018): Global non-monotonicity of solutions to nonlinear second-order differential equations. Mediterr. J. Math. 15, no. 2, Art.30, 17 pp.
Rab M. (1959): Kriterien für die Oszillation der Lösungen der Differentialgleichung $(p(x) y’)’+q(x)y=0$. (German) Časopis Pěst. Mat. 84, 335-370.
Wintner A. (1949): A criterion of oscillatory stability. Quart. Appl. Math. 7, 115-117.
Wintner A. (1950): A criterion for the nonexistence of $L^p$-solutions of a nonoscillatory differential equations. J. London Math. Soc. 25, 347-351.
Wong J. S. W., Burton T. A. (1965): Some properties of solutions of $u»(t)+a(t)f(u)g(u’)=0$. II. Monatsh. Math. 69, 368-374.
Wong J. S. W. (1967): Boundedness theorems for solutions of $u»(t)+a(t)f(u)g(u’)=0$, (IV) Enseignement Math. 2(13), 157-165.
Wyrwińska A. (1978): On the existence and non-existence of solutions of certai second order nonlinear differential equations in the class $Lsb{2}$. Fasc. Math. 10, 77-84.
Zlamal M. (1950): Oscillation criterions, Časopis Pěst. Mat. Fys. 75, 213-218.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Évkönyv
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Autorska prava: u cilju zaštite autorskih prava i izdavača, Učiteljski fakultet na mađarskom nastavnom jeziku, sa sedištem u Subotici, Univerzitet u Novom Sadu, štiti autorska prava u skladu sa zakonom, s tim da autori radova objavljenih u Godišnjaku mogu koristiti sopstvene članke i publikacije bez ograničenja.
