On the Unique Solvability of Certain Nonlinear Singular Partial Differential Equations
Jose Ernie C. LopeUniversity of the Philippines, Quezon City, Philippines
Marian P. RoqueUniversity of the Philippines, Quezon City, Philippines
Hidetoshi TaharaSophia University, Tokyo, Japan
We study the singular nonlinear equation , where the function is assumed to be continuous in and holomorphic in the other variables. Under some growth conditions on the coefficients of the partial Taylor expansion of , we show that if is of order for some as uniformly in some neighborhood of , then the equation has a unique solution with the same growth order.
Cite this article
Jose Ernie C. Lope, Marian P. Roque, Hidetoshi Tahara, On the Unique Solvability of Certain Nonlinear Singular Partial Differential Equations. Z. Anal. Anwend. 31 (2012), no. 3, pp. 291–305DOI 10.4171/ZAA/1461