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Sufficient Conditions for Uniqueness of Positive Solutions and Non Existence of Sign Changing Solutions for Elliptic Dirichlet Problems

Description: In this paper we study the uniqueness of positive solutions as well as the non existence of sign changing solutions for Dirichlet problems of the form $$\eqalign{\Delta u + g(\lambda,\ u) &= 0\quad\rm in\ \Omega,\cr u &= 0\quad\rm on\ \partial\Omega,}$$where $\Delta$ is the Laplace operator, $\Omega$ is a region in $\IR\sp{N}$, and $\lambda>0$ is a real parameter. For the particular function $g(\lambda,\ u)=\vert u\vert\sp{p}u+\lambda$, where $p={4\over N-2}$, and $\Omega$ is the unit ball in $… more
Date: August 1995
Creator: Hassanpour, Mehran
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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On Groups of Positive Type

Description: We describe groups of positive type and prove that a group G is of positive type if and only if G admits a non-trivial partition. We completely classify groups of type 2, and present examples of other groups of positive type as well as groups of type zero.
Date: August 1995
Creator: Moore, Monty L.
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Existence of a Sign-Changing Solution to a Superlinear Dirichlet Problem

Description: We study the existence, multiplicity, and nodal structure of solutions to a superlinear elliptic boundary value problem. Under specific hypotheses on the superlinearity, we show that there exist at least three nontrivial solutions. A pair of solutions are of one sign (positive and negative respectively), and the third solution changes sign exactly once. Our technique is variational, i.e., we study the critical points of the associated action functional to find solutions. First, we define a codi… more
Date: August 1995
Creator: Neuberger, John M. (John Michael)
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Steepest Sescent on a Uniformly Convex Space

Description: This paper contains four main ideas. First, it shows global existence for the steepest descent in the uniformly convex setting. Secondly, it shows existence of critical points for convex functions defined on uniformly convex spaces. Thirdly, it shows an isomorphism between the dual space of H^{1,p}[0,1] and the space H^{1,q}[0,1] where p > 2 and {1/p} + {1/q} = 1. Fourthly, it shows how the Beurling-Denny theorem can be extended to find a useful function from H^{1,p}[0,1] to L_{p}[1,0] where p … more
Date: August 1995
Creator: Zahran, Mohamad M.
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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A Numerical Method for Solving Singular Differential Equations Utilizing Steepest Descent in Weighted Sobolev Spaces

Description: We develop a numerical method for solving singular differential equations and demonstrate the method on a variety of singular problems including first order ordinary differential equations, second order ordinary differential equations which have variational principles, and one partial differential equation.
Date: August 1995
Creator: Mahavier, William Ted
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Descriptions and Computation of Ultrapowers in L(R)

Description: The results from this dissertation are an exact computation of ultrapowers by measures on cardinals $\aleph\sb{n},\ n\in w$, in $L(\IR$), and a proof that ordinals in $L(\IR$) below $\delta\sbsp{5}{1}$ represented by descriptions and the identity function with respect to sequences of measures are cardinals. An introduction to the subject with the basic definitions and well known facts is presented in chapter I. In chapter II, we define a class of measures on the $\aleph\sb{n},\ n\in\omega$, in … more
Date: August 1995
Creator: Khafizov, Farid T.
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Physical Motivation and Methods of Solution of Classical Partial Differential Equations

Description: We consider three classical equations that are important examples of parabolic, elliptic, and hyperbolic partial differential equations, namely, the heat equation, the Laplace's equation, and the wave equation. We derive them from physical principles, explore methods of finding solutions, and make observations about their applications.
Date: August 1995
Creator: Thompson, Jeremy R. (Jeremy Ray)
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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