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2013 On Complex Singularity Analysis for Some Linear Partial Differential Equations in 3
A. Lastra, S. Malek, C. Stenger
Abstr. Appl. Anal. 2013: 1-30 (2013). DOI: 10.1155/2013/394564


We investigate the existence of local holomorphic solutions Y of linear partial differential equations in three complex variables whose coefficients are holomorphic on some polydisc in 2 outside some singular set Θ . The coefficients are written as linear combinations of powers of a solution X of some first-order nonlinear partial differential equation following an idea, we have initiated in a previous work (Malek and Stenger 2011). The solutions Y are shown to develop singularities along Θ with estimates of exponential type depending on the growth's rate of X near the singular set. We construct these solutions with the help of series of functions with infinitely many variables which involve derivatives of all orders of X in one variable. Convergence and bounds estimates of these series are studied using a majorant series method which leads to an auxiliary functional equation that contains differential operators in infinitely many variables. Using a fixed point argument, we show that these functional equations actually have solutions in some Banach spaces of formal power series.


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A. Lastra. S. Malek. C. Stenger. "On Complex Singularity Analysis for Some Linear Partial Differential Equations in 3 ." Abstr. Appl. Anal. 2013 1 - 30, 2013.


Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1295.35013
MathSciNet: MR3126755
Digital Object Identifier: 10.1155/2013/394564

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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