Form of solutions to quadratic trinomial partial differential equations with two complex variables
DOI:
https://doi.org/10.58997/ejde.2024.23Abstract
This article describes the from of entire solutions to quadratic trinomial partial differential equations (PDEs). By applying the Nevanlinna theory and the characteristic equation of PDEs, we extend some of the results obtained in [24]. We also provide examples that illustrate our results.
For more information see https://ejde.math.txstate.edu/Volumes/2024/23/abstr.html
References
F. Gross; On the equation fn + gn = 1, Bull. Am. Math. Soc., 72 (1966), 86-88.
P. C. Hu, B. Q. Li; On meromorphic solutions of nonlinear partial differential equations of first order, J. Math. Anal. Appl., 377 (2011), 881-888.
D. Khavinson; A note on entire solutions of the eiconal equation, Am. Math. Mon., 102 (1995), 159-161.
B. Q. Li; Entire solutions of certain partial differential equations and factorization of partial derivatives, Tran. Amer. Math. Soc., 357 (2004), 3169-3177.
B. Q. Li; Entire solutions of eiconal type equations, Arch. Math., 89 (2007), 350-357.
B. Q. Li; Entire solutions of (uz1 )m + (uz2 )n = eg, Nagoya Math. J., 178 (2005), 151-162.
B. Q. Li; On entire solutions of Fermat type partial differential equations, Int. J. Math., 15 (2004), 473-485.
K. Liu, T. B. Cao, H. Z. Cao; Entire solutions of Fermat type differential-difference equations, Arch. Math., 99 (2012), 147-155.
K. Liu, L. Z. Yang; A note on meromorphic solutions of Fermat-types equations, An. SCtiintC. Univ. Al. I. Cuza IaCsi Mat.(N. S.), 2 (2016), 317-325.
F. LNu; Entire solutions of a variation of the eikonal equation and related PDEs, P. Edinburgh. Math. Soc., 68 (2020), 697-708.
F. LNu, Z. Li; Meromorphic solutions of Fermat type partial differential equations, J. Math. Anal. Appl., 478 (2019), 864-873.
P. Montel; Lecons sur les familles normales de fonctions analytiques et leurs applications, pp.135.sC136. Gauthier-Villars, Paris, 1927.
G. PLolya; On an integral function of an integral function, J. Lond. Math. Soc., 1 (1926), 12-15.
L. I. Ronkin; Introduction to the theory of entire functions of several variables, American Mathematical Soc., Vol. 44, 1974.
E. G. Saleeby; Entire and meromorphic solutions of Fermat type partial differential equations, Analysis 19 (1999), 369-376.
E. G. Saleeby; On complex analytic solutions of certain trinomial functional and partial differential equations, Aequat. Math., 85 (2013), 553-562.
W. Stoll; Holomorphic functions of finite order in several complex variables Conf. Board Math, Sci. Regional Conf. Ser. Math., Vol. 21, 1974.
R. Taylor, A. Wiles; Ring-theoretic properties of certain Hecke algebra, Ann. Math., 141 (1995), 553-572.
A. Wiles; Modular elliptic curves and Fermats last theorem, Ann. Math., 141 (1995), 443-551.
H. Y. Xu, G. Haldar; Solutions of complex nonlinear functional equations including second order partial differential and difference in C2, Electron. J. Differential Equations., 43(2023), 1-18.
H. Y. Xu, Y. Y. Jiang; Results on entire and meromorphic solutions for several systems of quadratic trinomial functional equations with two complex variables, Revista de la Real Academia de Ciencias Exactas, F.sasicas y Naturales. Serie A. Matem.sticas, 116 (2022) , no. 8, pp. 1-19.
H. Y. Xu, X. L. Liu, Y. H. Xu; On solutions for several systems of complex nonlinear partial differential equations with two variables, Anal. Math. Phys., 13 (2023), no. 47, pp. 1-24.
H. Y. Xu, D. W. Meng, S. Y. Liu, H. Wang; Entire solutions for several second-order partial differential-difference equations of Fermat type with two complex variables, Advances in Difference Equations, 2021, Art.52
H. Y. Xu, J. Tu, H. Wang; Transcendental entire solutions of several Fermat type PDEs and PDDEs with two complex variables, Rocky Mountain J. Math., 51 (2021), 2217-2235.
H. Y. Xu, L. Xu; Transcendental entire solutions for several quadratic binomial and trinomial PDEs with constant coefficients, Anal. Math. Phys., 12 (2022), 64.
H. Y. Xu, K. Y. Zhang, X. M. Zheng; Entire and meromorphic solutions for several Fermat type partial differential difference equations in C2, Rocky Mountain J. Math., 52 (2022), 2169-2187.
Downloads
Published
License
Copyright (c) 2024 Jin Tu, Huizhen Wei
This work is licensed under a Creative Commons Attribution 4.0 International License.
