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

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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)

Recommended Citations

Citations

  • Zhang, L. (2011). The Painlevé property and nonintegrability; The Dirichlet Boundary Value Problem for Complex Monge-Ampére Type Equation [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1313540635

    APA Style (7th edition)

  • Zhang, Lizhi. The Painlevé property and nonintegrability; The Dirichlet Boundary Value Problem for Complex Monge-Ampére Type Equation. 2011. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1313540635.

    MLA Style (8th edition)

  • Zhang, Lizhi. "The Painlevé property and nonintegrability; The Dirichlet Boundary Value Problem for Complex Monge-Ampére Type Equation." Doctoral dissertation, Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1313540635

    Chicago Manual of Style (17th edition)