Electron. J. Diff. Equ., Vol. 2015 (2015), No. 56, pp. 1-6.

A new proof of Borel's lemma in two dimensions

Dening Li

Existence of solutions for nonlinear problems can often be established by a Newton's scheme, near an approximate solution, combined with a regularization procedure. This article provides a new method of constructing an infinite order $C^\infty$ approximate solution for proving Borel's Lemma, without using the usual $C^\infty$ cut-off functions.

Submitted March 18, 2014. Published February 27, 2015.
Math Subject Classifications: 35L50, 40C05.
Key Words: Borel's Lemma; infinite order approximate solution.

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Dening Li
Department of Mathematics
West Virginia University
Morgantown, WV 26506, USA
email: li@math.wvu.edu

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