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Thesis_XiaoyueXia.pdf (1.13 MB)

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New asymptotic methods for the global analysis of ordinary differential equations and for non-selfadjoint spectral problems

Xia, Xiaoyue
http://rave.ohiolink.edu/etdc/view?acc_num=osu1437062908

Abstract Details

2015, Doctor of Philosophy, Ohio State University, Mathematics.
In this thesis we employ new asymptotic methods to study some problems in classical analysis and mathematical physics. The first problem is finding the global behavior in the complex plane of a class of analytic functions from the Taylor coefficients. Several explicit examples are presented, from which it is clear that combined with Laplace transformation and Borel transformation, the method has great potential in analyzing the solutions of differential equations. In the second problem we use methods originating from exponential asymptotics to study a non-selfajoint spectral problem in mathematical physics. In the third problem, tronquée solutions and tritronquée solutions of the third and fourth Painlevé equation are studied using the theory of Borel summation for analytic nonlinear rank one system of ODE's, which has been studied extensively in [2], [3] and [5].
Ovidiu Costin (Advisor)
Rodica Costin (Committee Member)
Saleh Tanveer (Committee Member)
168 p.
Mathematics

Recommended Citations

Citations

  • Xia, X. (2015). New asymptotic methods for the global analysis of ordinary differential equations and for non-selfadjoint spectral problems [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1437062908

    APA Style (7th edition)

  • Xia, Xiaoyue. New asymptotic methods for the global analysis of ordinary differential equations and for non-selfadjoint spectral problems. 2015. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1437062908.

    MLA Style (8th edition)

  • Xia, Xiaoyue. "New asymptotic methods for the global analysis of ordinary differential equations and for non-selfadjoint spectral problems." Doctoral dissertation, Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1437062908

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.