The Resource Positive solutions of nonlinear elliptic equations in the Euclidean plane, by Ünal Ufuktepe
Positive solutions of nonlinear elliptic equations in the Euclidean plane, by Ünal Ufuktepe
Resource Information
The item Positive solutions of nonlinear elliptic equations in the Euclidean plane, by Ünal Ufuktepe represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 2 library branches.
Resource Information
The item Positive solutions of nonlinear elliptic equations in the Euclidean plane, by Ünal Ufuktepe represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 2 library branches.
 Summary
 In the present thesis, we study the existence of solutions to the problem $\Delta u+f(x,u)=0$ in D $u>0$ in D $u=0$ on $\partial D$ (0.1) where D is an unbounded domain in $\IR\sp2$ with a compact nonempty boundary $\partial D$ consisting of finitely many Jordan curves. The goal is to prove an existence theorem for problem (0.1) in a general setting by using Brownian path integration and potential theory. In the first chapter, we provide the necessary background for the following chapters. The second chapter is devoted to the FeynmanKac functional, Schrodinger equations, and the conditional Brownian motion. In the third chapter, we first introduce the positive harmonic function in D with the specified behavior around $\partial D$ and $\{\infty\}.$ We prove the uniform integrability of the family of functions $\{G\sb{D}(x,.)\vert q(.):x\in D\}$ for a function q belonging to a general class $K\sbsp{2}{\infty},$ where $G\sb{D}(.,.)$ is the Green function in D. Finally we prove the main theorem which solves problem (0.1) under certain conditions on f
 Language
 eng
 Label
 Positive solutions of nonlinear elliptic equations in the Euclidean plane
 Title
 Positive solutions of nonlinear elliptic equations in the Euclidean plane
 Statement of responsibility
 by Ünal Ufuktepe
 Title variation
 Solutions on nonlinear elliptic equations
 Language
 eng
 Summary
 In the present thesis, we study the existence of solutions to the problem $\Delta u+f(x,u)=0$ in D $u>0$ in D $u=0$ on $\partial D$ (0.1) where D is an unbounded domain in $\IR\sp2$ with a compact nonempty boundary $\partial D$ consisting of finitely many Jordan curves. The goal is to prove an existence theorem for problem (0.1) in a general setting by using Brownian path integration and potential theory. In the first chapter, we provide the necessary background for the following chapters. The second chapter is devoted to the FeynmanKac functional, Schrodinger equations, and the conditional Brownian motion. In the third chapter, we first introduce the positive harmonic function in D with the specified behavior around $\partial D$ and $\{\infty\}.$ We prove the uniform integrability of the family of functions $\{G\sb{D}(x,.)\vert q(.):x\in D\}$ for a function q belonging to a general class $K\sbsp{2}{\infty},$ where $G\sb{D}(.,.)$ is the Green function in D. Finally we prove the main theorem which solves problem (0.1) under certain conditions on f
 Additional physical form
 Also available on the Internet.
 Cataloging source
 MUU
 http://library.link/vocab/creatorDate
 1960
 http://library.link/vocab/creatorName
 Ufuktepe, Ünal
 Degree
 Ph. D.
 Dissertation year
 1996.
 Government publication
 government publication of a state province territory dependency etc
 Granting institution
 University of MissouriColumbia
 Index
 no index present
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/subjectName

 Nonlinear theories
 Markov processes
 Brownian motion processes
 Schrödinger equation
 Target audience
 specialized
 Label
 Positive solutions of nonlinear elliptic equations in the Euclidean plane, by Ünal Ufuktepe
 Note

 Typescript
 Vita
 Bibliography note
 Includes bibliographical references (leaves 3940)
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Control code
 39302187
 Dimensions
 29 cm
 Dimensions
 unknown
 Extent
 iii, 41 leaves
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Specific material designation
 remote
 Label
 Positive solutions of nonlinear elliptic equations in the Euclidean plane, by Ünal Ufuktepe
 Note

 Typescript
 Vita
 Bibliography note
 Includes bibliographical references (leaves 3940)
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Control code
 39302187
 Dimensions
 29 cm
 Dimensions
 unknown
 Extent
 iii, 41 leaves
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Specific material designation
 remote
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Positivesolutionsofnonlinearelliptic/8vTFcMzOEkU/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Positivesolutionsofnonlinearelliptic/8vTFcMzOEkU/">Positive solutions of nonlinear elliptic equations in the Euclidean plane, by Ünal Ufuktepe</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>