Properties of entire solutions of some linear PDE's

• Autorzy: Bandura A , Skaskiv O. , Filevych P.

Identyfikatory

DOI

10.17512/jamcm.2017.2.02

• Języki publikacji: EN

Abstrakty

EN

In this paper, there are improved sufficient conditions of boundedness of the L-index in a direction for entire solutions of some linear partial differential equations. They are new even for the one-dimensional case and L≡1. Also, we found a positive continuous function l such that entire solutions of the homogeneous linear differential equation with arbitrary fast growth have a bounded l -index and estimated its growth.

Słowa kluczowe

EN

linear partial differential equation; entire function; bounded L-index in direction; bounded l-index; homogeneous linear differential equation; growth of solutions

PL

liniowe równanie różniczkowe cząstkowe; funkcja całkowita; równanie różniczkowe cząstkowe

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2017
• Tom: Vol. 16, nr 2
• Strony: 17--28
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Bandura A

• Department of Advanced Mathematics, Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine

autor

Skaskiv O.

• Department of Function Theory and Theory of Probability, Ivan Franko National University of Lviv Lviv, Ukraine

autor

Filevych P.

• Department of Information Technologies, Vasyl Stephanyk Precarpathional National University Ivano-Frankivsk, Ukraine

Bibliografia

• [1] Bandura A.I., Skaskiv O.B., Entire functions of bounded L-index in direction, Mat. Stud. 2007, 27, 1, 30-52 (in Ukrainian).
• [2] Bandura A.I., Skaskiv O.B., Sufficient sets for boundedness L -index in direction for entire functions, Mat. Stud. 2007, 30, 2, 30-52.
• [3] Bandura A.I., Skaskiv O.B., Open problems for entire functions of bounded index in direction, Mat. Stud. 2015, 43, 1, 103-109. dx.doi.org/10.15330/ms.43.1.103-109.
• [4] Bandura A., Skaskiv O., Entire functions of several variables of bounded index, Lviv, Chyslo, Publisher I.E. Chyzhykov 2016, 128 p.
• [5] Kuzyk A.D., Sheremeta M.M., Entire functions of bounded l -distribution of values, Math. Notes 1986, 39, 1, 3-8.
• [6] Kuzyk A.D., Sheremeta M.N., On entire functions, satisfying linear differential equations, Diff. Equations 1990, 26, 10, 1716-1722. (in Russian).
• [7] Fricke G.H., Shah S.M., Entire functions satisfying a linear differential equation, Indag. Math. 1975, 37, 39-41.
• [8] Fricke G.H., Shah S.M., On bounded value distribution and bounded index Nonlinear Anal. 1978, 2, 4, 423-435.
• [9] Bordulyak M.T., On the growth of entire solutions of linear differential equations, Mat. Stud. 2000, 13, 2, 219-223.
• [10] Cao T.-B., Complex oscillation of entire solutions of higher-order linear differential equations, Electronic Journal of Differential Equations 2006, 81, 1-8.
• [11] Chen Z.X., Yang C.C., Quantitative estimations on the zeros and growth of entire solutions of linear differential equations, Complex Variables 2000, 42, 119-133.
• [12] Hamani K., Belaїdi B., Growth of solutions of complex linear differential equations with entire coefficients of finite iterated order, Acta Universitatis Apulensis 2011, 27, 203-216.
• [13] Heittokangas J., Korhonen R., Rattya J., Growth estimates for analytic solutions of complex linear differential equations, Ann. Acad. Sci. Fenn. Math. 2004, 29, 233-246.
• [14] Kinnunen L., Linear differential equations with solutions of finite iterated order, Southeast Asian Bull. Math. 1998, 22, 385-405.
• [15] Lin J., Tu J., Shi L.Z., Linear differential equations with entire coefficients of [ p; q] -order in the complex plane, J. Math. Anal. Appl. 2010, 372, 55-67.
• [16] Chyzhykov I., Semochko N., Fast growing enitre solutions of linear differential equations, Math. Bull. Shevchenko Sci. Soc. 2016, 13, 68-83.
• [17] Sheremeta M., Analytic Functions of Bounded Index, VNTL Publishers, Lviv 1999, 142 p.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).