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Titlebook: Variational, Topological, and Partial Order Methods with Their Applications; Zhitao Zhang Book 2013 Springer-Verlag Berlin Heidelberg 2013

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Variational, Topological, and Partial Order Methods with Their Applications978-3-642-30709-6Series ISSN 1389-2177 Series E-ISSN 2197-795X
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1389-2177 near functional analysis is an important branch of contemporary mathematics. It‘s related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry, measure theory, and more. In this book, the author presents some new and interesti
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Topological Methods and Applications,xistence of solutions, and apply them to two-point boundary problems of systems of equations. We also are concerned with the existence of (component-wise) positive solutions for a semilinear elliptic system, where the nonlinear term is superlinear in one equation and sublinear in the other equation.
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Nonlocal Kirchhoff Elliptic Problems,ps, and we obtain sign-changing solutions of a class of nonlocal quasilinear elliptic boundary value problems using variational methods and invariant sets of descent flows. We also show a uniqueness result.
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,Free Boundary Problems, System of Equations for Bose–Einstein Condensate and Competing Species,e existence and uniqueness result of the Dirichlet boundary value problem of elliptic competing systems. We show that, for the singular limit, species are spatially segregated; they satisfy a remarkable system of differential inequalities as .→+∞. We also introduce optimal partition problems related
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,Free Boundary Problems, System of Equations for Bose–Einstein Condensate and Competing Species, are spatially segregated; they satisfy a remarkable system of differential inequalities as .→+∞. We also introduce optimal partition problems related to eigenvalues and nonlinear eigenvalues. Finally, some recent new results on Schrödinger systems from Bose–Einstein condensates are presented.
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