以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：160

、訪客IP：18.216.251.37

姓名	吳彥霖(Yen-Lin Wu)  查詢紙本館藏	畢業系所	數學系
論文名稱	探討源自於隨機最佳化控制問題之偏微分方程與其相關應用 (Solutions of Partial Differential Equations Arising from Stochastic Optimal Control Problems and Applications)
相關論文	★ 薛丁格方程式上直立波解的分類。 ★ Conformality of Planar Parameterization for Single Boundary Triangulated Surface Mesh ★ 混合噪聲的即時圖像去噪在螢光顯微鏡圖像和古畫中的應用 ★ 一些線性矩陣方程其平滑及週期的最小 l_2-解之探討 ★ 關於漢米爾頓矩陣的某些平滑性分解 ★ 在N維實數域之雙調和微分方程 ★ 一維動態系統其週期解之研究 ★ 一些延滯方程其週期解之探討 ★ On the Blow-up solutions of Biharmonic Equation on a ball ★ 雙調和微分方程其正整域解的存在性與不存在性之探討 ★ 高階橢圓偏微分方程解的存在性及其行為之研究 ★ 有絲分裂中染色體運動之動態分析 ★ 非線性橢圓方程及系統中解的唯一性和結構性之探討 ★ On the Positive Solution for Grad-Shafranov Equation ★ 關於三物種間之高流動性Lotka-Vollterra競爭擴散系統的波形極限行為 ★ 非線性橢圓型偏微分方程系統之解結構分析
檔案	[Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   [檢視]  [下載] 本電子論文使用權限為同意立即開放。 已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。 請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。
摘要(中)	本論文主要探討三種不同型態之二階非線性橢圓偏微分方程式，其解的存在性、唯一性與結構性之相關定性分析及研究。第一部分中，我們考慮一個與隨機最佳化控制問題(stochastic optimal control problem)相關之方程，其具所謂『梯度約束方程式(gradient constraint equation)』之型態；在其非線性項更加弱化的條件下，我們證得其正解之存在性與唯一性。第二部分中，我們考慮一個座落於雙曲空間(hyperbolic space)中之半線性橢圓偏微分方程；研究其正奇異解在原點的漸近行為並且提供此正奇異解之存在性與唯一性；除此之外，我們透過『Pohozaev恆等式』了解其他不同型態解之特性，藉此進一步獲得某些特定型態解之不存在性。最後，在第三部分中我們考慮所謂的『Hardy-Sobolev方程』；在不同的指數條件下，我們研究其解的存在性、唯一性以及原點或無窮遠之行為。
摘要(英)	This dissertation is concerned with studying some second order elliptic partial differential equations. We are devote to establishing some qualitative properties of solutions, including existence, uniqueness and structure of solutions to three specific types of nonlinear elliptic equations. In Part 1, we study a gradient constraint equation which is related to a stochastic optimal control problem. We offer the existence and uniqueness of positive radial solutions with certain behavior under weaker conditions on nonlinearity. In Part 2, we consider a semilinear elliptic equation on the hyperbolic space. The asymptotic behavior, existence and uniqueness of positive singular solutions at the origin are proved. In addition, we discuss the structure of solutions of various types via the Pohozaev identity. Finally, in our last chapter, we deal with the Hardy-Sobolev equations and investigate behaviors, existence and uniqueness of solutions for different exponents.
關鍵字(中)	★ 二階橢圓偏微分方程 ★ 隨機最佳化控制問題 ★ 存在性 ★ 唯一性	關鍵字(英)	★ Partial Differential Equations ★ Stochastic Optimal Control Problems ★ Existence ★ Uniqueness
論文目次	Preface i 1 Gradient Constraint Elliptic Equations 1 1.1 Introduction . . . . . . . . . . . . 2 1.2 Preliminaries . . . . . . . . . . . 7 1.3 Existence and Uniqueness of Solutions . . . . . . . 13 2 Semilinear Elliptic Equations on the Hyperbolic Space 19 2.1 Introduction . . . . . . . . . . . . 20 2.2 Preliminaries . . . . . . . . . . . 22 2.3 Existence and Uniqueness: Positive Singular Solution . . . . . 30 2.4 Behaviors and Nonexistence of Solutions . . . . . . 34 3 Hardy-Sobolev Equations 47 3.1 Introduction . . . . . . . . . . . . 48 3.2 Preliminaries . . . . . . . . . . . 52 3.3 Nonexistence of Solutions . . . . . . . . . . 59 3.4 Proofs of Main Results . . . . . . . . . . 62 Bibliography 69
參考文獻	[1] S. Bae, Separation structure of positive radial solutions of a semilinear elliptic equation in R^n, J. Differential Equations 194 (2003), 460-499. [2] S. Bae and T. K. Chang, On a class of semilinear elliptic equations in R^n, J. Differential Equations 185 (2002), 225-250. [3] C. Bandle, A. Brillard and M. Flucher, Green′s function, harmonic transplantation and best Sobolev constant in spaces of constant curvature, Trans. Amer. Math. Soc. 350 (1998), 1103-1128. [4] C. Bandel and M. Essen, On the positive solutions of Emden equations in cone-like domains, Arch. Rational Mech. Anal. 112 (1990), 319-338. [5] C. Bandle and Y. Kabeya, On the positive, ``radial" solutions of a semilinear elliptic equation on H^N, Adv. Nonlinear Anal. 1 (2012), 1-25. [6] C. Bandle and H. A. Levine, On the existence and nonexistence of global solutions of reaction-diffusion equations in sectorial domains, Trans. Amer. Math. Soc. 316 (1989), 595-622. [7] C. Bandle and M. Marcus, The positive radial solutions of a class of semilinear elliptic equations, J. Reine Angew. Math. 401 (1989), 25-59. [8] M. Bonforte, F. Gazzola, G. Grillo and J. L. Vazquez, Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space, to appear. [9] H. Br´ezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving crtical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 437–477. [10] J.-L. Chern, Z.-Y. Chen, J-H. Chen and Y.-L. Tang, On the classification of standing wave solutions for the Schr¨odinger equation, Comm. Partial Differential Equations 35 (2010), 275–301; Erratum in Comm. Partial Differential Equations 35 (2010), 1920–1921. [11] J.-L. Chern, Z.-Y. Chen and Y.-L. Tang, Uniqueness of finite total curvatures and the structure of radial solutions for nonlinear elliptic equations, Transactions of the American Mathematical Society 363 (2011), 3211–3231. [12] J.-L. Chern and C.-S. Lin, Minimizers of Caffarelli-Kohn-Nirenberg inequalities on domains with the singularity on the boundary, Arch. Ration. Mech. Anal. 197 (2010), 401–432. [13] M. Davis and R. Norman, Portfolio selection with transaction costs, Mathematics of Operations Research 15 (1990) no. 4, 676–713. [14] M. Davis, V. Panas and T. Zariphopoulou, European option pricing under transaction fees, SIAM J. Cont. Opt. 31 (1993), 470–493. [15] W.-Y. Ding and W.-M. Ni, On the elliptic equation Δu + Ku(n+2)=(n−2) = 0 and related topics, Duke Math. J. 52 (1985), 485–486. [16] H. Egnell, Positive solutions of semilinear equations in Cones, Trans. Amer. Math. Soc. 11 (1992), 191–201. [17] L. C. Evans, A second-order elliptic equation with gradient constraint, Comm. Partial Differential Equations 4 (1979), no. 5, 555–572. [18] L. C. Evans, Correction to: ”A second-order elliptic equation with gradient constraint”, Comm. Partial Differential Equations 4 (1979), no. 10, 1199. [19] A. Friedman, Variational principles and free-boundary problems, Second edition. Robert E. Krieger Publishing Co., Inc., Malabar, FL, 1988. [20] N. Ghoussoub and X.S. Kang, Hardy-Sobolev Critical elliptic equations with boundary singularities, Ann. Inst. H. Poincar´e Anal. Non Linaire 21 (2004), 767–793. [21] N. Ghoussoub and C. Yuan, Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents, Trans. Amer. Math. Soc. 12 (2000), 5703– 5743. [22] B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209–243. [23] B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry of posiive solutions of nonlinear elliptic equations in Rn, Adv. Math. Suppl. Stud. 7A (1981), 369–402. [24] B. Gidas and J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 34 (1981), 525–598. [25] A. Grigor’yan, “Heat kernel and analysis on manifolds”, AMS, Providence, (2009). [26] C. Gui, W.-M. Ni and X.-F. Wang, On the stability and instability of positive steady states of a semilinear heat equation in Rn, Comm. Pure Appl. Math. 45 (1992), 1153–1181. [27] P. Hartman, “Ordinary differential equations”, Birkh¨auser Basel (1982), second edition. [28] R. Hynd, The eigenvalue problem of singular ergodic control, Communications on Pure and Applied Mathematics 65 (2012), 0649–0682. [29] R. Hynd, Analysis of Hamilton-Jacobi-Bellman equations arising in Stochastic singular control, ESAIM: Control Optim. Calc. Var. 19 (2013), no. 1, 112–128. [30] H. Ishii and S. Koike, Boundary regularity and uniqueness for an elliptic equation with gradient constraint, Comm. Partial Differential Equations 8 (1983), no. 4, 317– 346. [31] D. D. Joseph and T. S. Lundgren, Quasilinear Dirichlet problems driven by positive sources, Arch. Rational Mech. Anal. 49 (1973), 241–269. [32] N.J. Kruk, Optimal policies for n-dimensional singular stochastic control problems. Part II: The radially symmetric case. Ergodic control, SIAM J. Control Optim 39 (2000), no. 2, 635–659. [33] S. Kumaresan and J. Prajapat, Analogue of Gidas-Ni-Nirenberg result in hyperbolic space and sphere, Rend. Inst. Math. Univ. Trieste 30 (1998), 107–112. [34] Y. Li, Asymptotic behavior of positive solutions of equation Δu + K(x)up = 0 in Rn, J. Differential Equations 95 (1992), 304-330. [35] C.-S. Lin and Z.-Q. Wang, Symmetry of extremal functions for the Caffarelli-Kohn- Nirenberg inequalities, Proc. Amer. Math. Soc. 132 (2004), 1685–1691. [36] P.-L. Lions, The concentration-compactness principle in the calculus of variations. The limit case. I, Riv. Mat. Iberoamericana 1 (1985), no. 1, 145–201. [37] P.-L. Lions, The concentration-compactness principle in the calculus of variations. The limit case. II, Riv. Mat. Iberoamericana 1 (1985), no. 2, 45–121. [38] Y. Liu, Y. Li, and Y. Deng, Separation property of solutions for a semilinear elliptic equation, J. Differential Equations 163 (2000), 381–406. [39] G. Mancini and K. Sandeep, On a semilinear elliptic equation in Hn, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), 7 (2008), 635–671. [40] J.-L. Menaldi, M. Robin and M. Taksar, Singular ergodic control for multidimensional Gaussian processes, Math. Control Signals Systems 5 (1992), no. 1, 93–114. [41] W.-M. Ni, On the positive radial solutions of some semilinear elliptic equations on Rn, Appl. Math. Optim. 9 (1983), 373–380. [42] W.-M. Ni and S. Yotsutani, Semilinear elliptic equations of Matukuma-type and related topics, Japan J. Appl. Math. 5 (1988), 1–32. [43] P. Passaseo, Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains, Manuscripta Math. 65 (1989), 147–165. [44] H. M. Soner and S. E. Shreve, Regularity of the value function for a two-dimensional singular stochastic control problem, SIAM J. Control Optim. 27 (1989), no. 4, 876– 907. [45] S. Stapelkamp, The Brezis-Nirenberg problem on Hn: existence and uniqueness of solutions in “ Elliptic and Parabolic Problems- Rolduc and Gaeta 2001”, Bemelmans et al. ed., World Scientific Publ. River Edge, NJ, (2002), 283–290. [46] X.-F. Wang, On Cauchy Problem for reaction-diffusion equations, Trans. Amer. Math. Soc. 337 (1993), 549–590. [47] M. Wiegner, The C1−1-character of solutions of second order elliptic equations with gradient constraint, Comm. Partial Differential Equations 6 (1981), no. 3, 361–371.
指導教授	陳建隆(Jann-Long Chern)	審核日期	2014-7-7
推文	facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu
網路書籤	Google bookmarks   del.icio.us   hemidemi   myshare