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Focuses on heat equations associated with non self-adjoint uniformly elliptic operators. This book provides introductory materials for those unfamiliar with the underlying mathematics and background needed to understand the properties of heat equations. It then treats Lp properties of solutions to a wide class of heat equations.

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Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-know Yamabe type.

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The description for this book, Contributions to the Theory of Partial Differential Equations. (AM-33), will be forthcoming.

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Explores developments in the theory of planar quasiconformal mappings with a focus on the interactions with partial differential equations and nonlinear analysis. This book presents a modern approach to the classical theory and features applications across a spectrum of mathematics such as dynamical systems and singular integral operators.

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The Neumann problem is probably the most important and natural example of a non-elliptic boundary value problem, arising as it does from the Cauchy-Riemann equations. It has been known for some time how to prove solvability and regularity by the use of L2 methods. In this monograph the authors apply recent methods involving the Heisenberg group

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The description for this book, Existence Theorems in Partial Differential Equations. (AM-23), will be forthcoming.

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This book considers problems arising the theory of differential equations. This book is not only intended for mathematicians specializing in the theory of differential equations or in probability theory but also for specialists in asymptotic methods and functional analysis.

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Presents an overview of the developments in the area of localization for quasi-periodic lattice Schrodinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations. This book emphasises on so-called 'non-perturbative' methods and the role of subharmonic function theory and semi-algebraic set methods.

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Serves as a text for mathematics students at the intermediate graduate level. This book aims to acquaint readers with the fundamental classical results of partial differential equations and to guide them into some aspects of the modern theory to the point where they will be equipped to read advanced treatises and research papers.

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Mathematical Notes, 29 Originally published in 1983. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paper

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A collection of papers on mathematical aspects of nonlinear dispersive equations, including both expository and technical papers that reflect a number of advances in the field. The expository papers describe the state of the art and research directions. The technical papers concentrate on a specific problem and the related analysis.

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Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms.

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Book 22 in the Princeton Mathematical Series. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presentin

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(Hardback)

Covers stability and stabilization of equilibria for both linear and nonlinear time-invariant systems of ordinary differential equations. Suitable for advanced undergraduates and beginning graduate students in the sciences, engineering, and mathematics, this book takes a modern approach that bridges the gap between linear and nonlinear systems.

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This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian. These methods constitute, in part, an extension to partial differential equations of the method of symplectic geometry and Hamilton-Jacobi theory for Lagrangian systems of ordinary differential equations.

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