{"title":"Julian Lopez-Gomez","description":null,"products":[{"product_id":"linear-second-order-elliptic-operators-book-julian-lopez-gomez-9789814440240","title":"Linear Second Order Elliptic Operators","description":"The main goal of the book is to provide a comprehensive and self-contained proof of the, relatively recent, theorem of characterization of the strong maximum principle due to Molina-Meyer and the author, published in Diff. Int. Eqns. in 1994, which was later refined by Amann and the author in a paper published in J. of Diff. Eqns. in 1998. Besides this characterization has been shown to be a pivotal result for the development of the modern theory of spatially heterogeneous nonlinear elliptic and parabolic problems; it has allowed us to update the classical theory on the maximum and minimum principles by providing with some extremely sharp refinements of the classical results of Hopf and Protter-Weinberger. By a celebrated result of Berestycki, Nirenberg and Varadhan, Comm. Pure Appl. Maths. in 1994, the characterization theorem is partially true under no regularity constraints on the support domain for Dirichlet boundary conditions.Instead of encyclopedic generality, this book pays special attention to completeness, clarity and transparency of its exposition so that it can be taught even at an advanced undergraduate level. Adopting this perspective, it is a textbook; however, it is simultaneously a research monograph about the maximum principle, as it brings together for the first time in the form of a book, the most paradigmatic classical results together with a series of recent fundamental results scattered in a number of independent papers by the author of this book and his collaborators.Chapters 3, 4, and 5 can be delivered as a classical undergraduate, or graduate, course in Hilbert space techniques for linear second order elliptic operators, and Chaps. 1 and 2 complete the classical results on the minimum principle covered by the paradigmatic textbook of Protter and Weinberger by incorporating some recent classification theorems of supersolutions by Walter, 1989, and the author, 2003. Consequently, these five chapters can be taught at an undergraduate, or graduate, level. Chapters 6 and 7 study the celebrated theorem of Krein-Rutman and infer from it the characterizations of the strong maximum principle of Molina-Meyer and Amann, in collaboration with the author, which have been incorporated to a textbook by the first time here, as well as the results of Chaps. 8 and 9, polishing some recent joint work of Cano-Casanova with the author. Consequently, the second half of the book consists of a more specialized monograph on the maximum principle and the underlying principal eigenvalues.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52684433064209,"sku":"NLS9789814440240","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52764005302545,"sku":"NIN9789814440240","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789814440240.jpg?v=1762323017"},{"product_id":"spectral-theory-and-nonlinear-functional-analysis-book-julian-lopez-gomez-9781584882497","title":"Spectral Theory and Nonlinear Functional Analysis","description":"This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic\/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.  The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52684705104145,"sku":"NLS9781584882497","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53083551727889,"sku":"NIN9781584882497","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781584882497.jpg?v=1762323649"},{"product_id":"ordinary-differential-equations-linear-and-nonlinear-systems-dynamical-systems-a-book-julian-lopez-gomez-9789819811540","title":"Ordinary Differential Equations: Linear And Nonlinear Systems, Dynamical Systems And Applications","description":"The theory of ordinary differential equations is addressed in detail in this textbook, and is split into three sections: linear equations and systems, the general theory of nonlinear systems, and the theory of dynamical systems. These topics can be taken together or studied independently.In addition to standard materials on the theory of ordinary differential equations, this textbook specialises in covering non-standard materials related to this theory including  the theory of linear equation and systems with holomorphic coefficients; Kneser's theorem on the complexity of the set of solutions in the absence of uniqueness; the method of sub- and supersolutions for cooperative systems; and a detailed construction of the global bifurcation diagrams for some parametric classes of one-dimensional boundary value problems, which are pivotal for applications of the theory.This is a self-contained, rigorous treatment of ordinary differential equations that is complemented by a variety of illustrating examples of the theory in practice. Many of these examples are related to models in Physics and Applied Sciences, making them suitable for students in Physics, Chemistry, Engineering, Mathematical Biology, Economics and Ecology as well as in Mathematics. Each chapter contains exercises to test students' understanding of the topic and concludes with some historical notes and further discussions.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52772401479953,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52772402102545,"sku":"NLS9789819811540","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789819811540.jpg?v=1763772712"},{"product_id":"ordinary-differential-equations-linear-and-nonlinear-systems-dynamical-systems-a-book-julian-lopez-gomez-9789819812400","title":"Ordinary Differential Equations: Linear And Nonlinear Systems, Dynamical Systems And Applications","description":"The theory of ordinary differential equations is addressed in detail in this textbook, and is split into three sections: linear equations and systems, the general theory of nonlinear systems, and the theory of dynamical systems. These topics can be taken together or studied independently.In addition to standard materials on the theory of ordinary differential equations, this textbook specialises in covering non-standard materials related to this theory including  the theory of linear equation and systems with holomorphic coefficients; Kneser's theorem on the complexity of the set of solutions in the absence of uniqueness; the method of sub- and supersolutions for cooperative systems; and a detailed construction of the global bifurcation diagrams for some parametric classes of one-dimensional boundary value problems, which are pivotal for applications of the theory.This is a self-contained, rigorous treatment of ordinary differential equations that is complemented by a variety of illustrating examples of the theory in practice. Many of these examples are related to models in Physics and Applied Sciences, making them suitable for students in Physics, Chemistry, Engineering, Mathematical Biology, Economics and Ecology as well as in Mathematics. Each chapter contains exercises to test students' understanding of the topic and concludes with some historical notes and further discussions.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52772403183889,"sku":"NLS9789819812400","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53152781074705,"sku":"NIN9789819812400","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789819812400.jpg?v=1764843984"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-julian-lopez-gomez.oembed","provider":"World of Books ","version":"1.0","type":"link"}