The Painleve Property and Nonintegrability; The Dirichlet Boundry Value Problem for Complex Monge-Amphere Type Equation
We first show that one type of nonlinear first order differential equations are nonintegrable unless infinitely many conditions are met.The conditions are closely related to the Painleve test. (Roughly speaking, the Painleve test requires that generic solutions are single-valued, except at singular points of the equation.)More precisely we analyze first order nonlinear differential equations amenable to a standard form.
Later, we consider the Dirichlet boundary problem for Monge-Ampere type equations and show the existence of infinitely differentiable solution in the closure of a strictly pseudoconvex domain.
Lizhi Zhang Thesis.pdf