Jose Ernie C. Lope, Mark Philip F. Ona
Abstract:
We consider a system of equations composed of a higher order singular
partial differential equation of totally characteristic type and several
higher order non-Kowalevskian linear equations. This system is a higher
order version of a system that arose in Bielawski's investigations
on K\"ahler metrics. We first prove that this system has a unique
holomorphic solution. We then show that if the coefficients of the
system are in some formal Gevrey class, then the unique solution is
also in the same formal Gevrey class.
Submitted October 31, 2016. Published February 21, 2017.
Math Subject Classifications: 35G50, 35A20.
Key Words: Totally characteristic equation; singular partial differential equation;
majorant function; formal Gevrey class.
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Jose Ernie C. Lope Institute of Mathematics, College of Science University of the Philippines Diliman Quezon City, Philippines email: ernie@math.upd.edu.ph |
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Mark Philip F. Ona Institute of Mathematics, College of Science University of the Philippines Diliman Quezon City, Philippines email: mpona@math.upd.edu.ph |
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