05399nam 2200673Ia 450 991077701860332120200520144314.01-281-91949-79786611919498981-277-444-0(CKB)1000000000414553(EBL)1679587(OCoLC)879023827(SSID)ssj0000215971(PQKBManifestationID)11184951(PQKBTitleCode)TC0000215971(PQKBWorkID)10194020(PQKB)10505155(MiAaPQ)EBC1679587(WSP)00005999(Au-PeEL)EBL1679587(CaPaEBR)ebr10201447(CaONFJC)MIL191949(PPN)151504385(EXLCZ)99100000000041455320061002d2006 uy 0engur|n|---|||||txtccrOrder structure and topological methods in nonlinear partial differential equationsVolume 1Maximum principles and applications[electronic resource] /Yihong DuSingapore ;Hackensack, NJ World Scientificc20061 online resource (202 p.)Series on partial differential equations and applications ;v. 2Description based upon print version of record.981-256-624-4 Includes bibliographical references and index.Contents ; Preface ; 1. Krein-Rutman Theorem and the Principal Eigenvalue ; 2. Maximum Principles Revisited ; 2.1 Equivalent forms of the maximum principle ; 2.2 Maximum principle in W2N(O) ; 3. The Moving Plane Method ; 3.1 Symmetry over bounded domains3.2 Symmetry over the entire space 3.3 Positivity of nonnegative solutions ; 4. The Method of Upper and Lower Solutions ; 4.1 Classical upper and lower solutions ; 4.2 Weak upper and lower solutions ; 5. The Logistic Equation ; 5.1 The classical case5.2 The degenerate logistic equation 5.3 Perturbation and profile of solutions ; 6. Boundary Blow-Up Problems ; 6.1 The Keller-Osserman result and its generalizations ; 6.2 Blow-up rate and uniqueness ; 6.3 Logistic type equations with weights7. Symmetry and Liouville Type Results over Half and Entire Spaces 7.1 Symmetry in a half space without strong maximum principle ; 7.2 Uniqueness results of logistic type equations over RN ; 7.3 Partial symmetry in the entire space ; 7.4 Some Liouville type resultsAppendix A Basic Theory of Elliptic Equations A.l Schauder theory for elliptic equations ; A.2 Sobolev spaces ; A.3 Weak solutions of elliptic equations ; A.4 LP theory of elliptic equations ; A.5 Maximum principles for elliptic equations ; A.5.1 The classical maximum principlesA.5.2 Maximum principles and Harnack inequality for weak solutions The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems. The maximum principle is revisited through the use of the Krein-Rutman theorem and the principal eigenvalues. Its various versions, such as the moving plane and sliding plane methods, are applied to a variety of important problems of current interest. The upper and lower solution method, especSeries on partial differential equations and applications ;v. 2.Differential equations, NonlinearNumerical solutionsDifferential equations, PartialNumerical solutionsDifferential equations, NonlinearNumerical solutions.Differential equations, PartialNumerical solutions.515.353Du Yihongjin shi 1761.1557893MiAaPQMiAaPQMiAaPQBOOK9910777018603321Order structure and topological methods in nonlinear partial differential equations3821862UNINA