03288nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072002300184072001600207100007600223245010700299250001800406264007200424300004400496336002600540337002600566338003600592347002400628505050300652520115101155650002802306650002502334650002002359650002402379650002802403650002502431650004402456650002502500700007902525710003402604773002602638776003602664776003602700776003602736856004602772978-981-99-8692-7DE-He21320251030112014.0cr nn 008mamaa240426s2024    si |    s    |||| 0|eng d  a97898199869277 a10.1007/978-981-99-8692-72doi 4aQA370-380 7aPBKJ2bicssc 7aMAT0070002bisacsh 7aPBKJ2thema1 aWang, Mingxin.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aNonlinear Second Order Elliptic Equationsh[electronic resource] /cby Mingxin Wang, Peter Y. H. Pang.  a1st ed. 2024. 1aSingapore :bSpringer Nature Singapore :bImprint: Springer,c2024.  aXII, 314 p. 29 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aPreface -- Preliminaries -- Eigenvalue problems of second order linear elliptic operators -- Upper and lower solutions method for single equations -- Upper and lower solutions method for systems -- Theory of topological degree in cones and applications -- Systems with homogeneous Neumann boundary conditions -- P-Laplace equations and systems -- Appendix A: Basic results of Sobolev spaces and nonlinear functional analysis -- Appendix B: Basic theory of elliptic equations -- References -- Index.  aThis book focuses on the following three topics in the theory of boundary value problems of nonlinear second order elliptic partial differential equations and systems: (i) eigenvalue problem, (ii) upper and lower solutions method, (iii) topological degree method, and deals with the existence of solutions, more specifically non-constant positive solutions, as well as the uniqueness, stability and asymptotic behavior of such solutions. While not all-encompassing, these topics represent major approaches to the theory of partial differential equations and systems, and should be of significant interest to graduate students and researchers. Two appendices have been included to provide a good gauge of the prerequisites for this book and make it reasonably self-contained. A notable strength of the book is that it contains a large number of substantial examples. Exercises for the reader are also included. Therefore, this book is suitable as a textbook for graduate students who have already had an introductory course on PDE and some familiarity with functional analysis and nonlinear functional analysis, and as a reference for researchers. 0aDifferential equations. 0aFunctional analysis. 0aBiomathematics. 0aPopulation biology.14aDifferential Equations.24aFunctional Analysis.24aMathematical and Computational Biology.24aPopulation Dynamics.1 aPang, Peter Y. H.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978981998691008iPrinted edition:z978981998693408iPrinted edition:z978981998694140uhttps://doi.org/10.1007/978-981-99-8692-7