Multisummability of formal power series solutions of nonlinear partial differential equations in complex domains

被引:0
作者
Ouchi, S [1 ]
机构
[1] Sophia Univ, Dept Math, Chiyoda Ku, Tokyo 1028554, Japan
关键词
asymptotic expansion; formal power series solutions; multisummability;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let (u) over cap (t,x) = Sigma(infinity)(n=1) u(n)(x)t(n), (t,x) is an element of C x C-d, be a formal power series solution of a nonlinear partial differential equation. We study multisummability of (u) over cap (t,x). This paper is a continuation of [S. (O) over bar uchi, Multisummability of formal solutions of some linear partial differential equations, J. Differential Equations 185 (2002), 513-549], where linear partial differential equations were treated.
引用
收藏
页码:187 / 225
页数:39
相关论文
共 43 条
[21]   Gevrey Order and Summability of Formal Series Solutions of some Classes of Inhomogeneous Linear Partial Differential Equations with Variable Coefficients [J].
Remy, Pascal .
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2016, 22 (04) :693-711
[22]   ON THE MULTISUMMABILITY OF WKB SOLUTIONS OF CERTAIN SINGULARLY PERTURBED LINEAR ORDINARY DIFFERENTIAL EQUATIONS [J].
Takei, Yoshitsugu .
OPUSCULA MATHEMATICA, 2015, 35 (05) :775-802
[23]   EXPONENTIAL-TYPE NAGUMO NORMS AND SUMMABILITY OF FORMAL SOLUTIONS OF SINGULAR PARTIAL DIFFERENTIAL EQUATIONS [J].
Luo, Zhuangchu ;
Chen, Hua ;
Zhang, Changgui .
ANNALES DE L INSTITUT FOURIER, 2012, 62 (02) :571-618
[24]   Summability of formal solutions of a class of nonlinear difference equations [J].
Immink, GK .
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2001, 7 (01) :105-126
[25]   Delta series solutions of differential and integral equations [J].
Kanwal, RP .
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 1998, 6 (1-4) :49-62
[26]   Asymptotic existence theorems for formal power series whose coefficients satisfy certain partial differential recursions [J].
Balser, W .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 209 (02) :442-457
[27]   ACCELERO-SUMMATION OF THE FORMAL SOLUTIONS OF NONLINEAR DIFFERENCE EQUATIONS [J].
Immink, Geertrui Klara .
ANNALES DE L INSTITUT FOURIER, 2011, 61 (01) :1-51
[28]   A Remark on Approximation of the Solutions to Partial Differential Equations in Finance [J].
Takahashi, Akihiko ;
Yamada, Toshihiro .
RECENT ADVANCES IN FINANCIAL ENGINEERING 2011, 2012, :133-181
[29]   Asymptotic existence theorem for formal power series solutions of singularly perturbed linear q-difference equations [J].
Tahara, Hidetoshi .
MATHEMATISCHE ANNALEN, 2024, 390 (03) :3995-4039
[30]   Analytic and Summable Solutions of Inhomogeneous Moment Partial Differential Equations [J].
Michalik, Slawomir .
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2017, 60 (03) :325-351