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The Painlevé property and nonintegrability; The Dirichlet Boundary Value Problem for Complex Monge-Ampére Type Equation
Zhang, Lizhi

2011, Doctor of Philosophy, Ohio State University, Mathematics.

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.

Ovidiu Costin, Professor (Committee Chair)
Saleh Tanveer, Professor (Committee Member)
Rodica Costin, Professor (Committee Member)

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Zhang, L. (2011). The Painlevé property and nonintegrability; The Dirichlet Boundary Value Problem for Complex Monge-Ampére Type Equation. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Zhang, Lizhi. "The Painlevé property and nonintegrability; The Dirichlet Boundary Value Problem for Complex Monge-Ampére Type Equation." Electronic Thesis or Dissertation. Ohio State University, 2011. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Zhang, Lizhi "The Painlevé property and nonintegrability; The Dirichlet Boundary Value Problem for Complex Monge-Ampére Type Equation." Electronic Thesis or Dissertation. Ohio State University, 2011. https://etd.ohiolink.edu/

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