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, especially its weak version, is presented in its most up-to-date form with enough generality to cater for wide applications. Recent progress on the boundary blow-up problems and their applications are discussed, as well as some new symmetry and Liouville type results over half and entire spaces. Some of the results included here are published for the first time.
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weak lower solution, weak upper solution, moving plane method, bounded positive solution, strict supersolution, minimal positive solution, boundary lemma, strong maximum principle, upper solutions, unique positive solution, weak maximum principle, semilinear elliptic equations, one positive solution, quasilinear elliptic equations, principal eigenvalue, order interval, lower solutions, nonlinear elliptic equations, imbedding theorem, nonnegative solution, maximal solution, minimal solution Key Phrases - Capitalized Phrases (CAPs): (learn more)
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weak lower solution, weak upper solution, moving plane method, bounded positive solution, strict supersolution, minimal positive solution, boundary lemma, strong maximum principle, upper solutions, unique positive solution, weak maximum principle, semilinear elliptic equations, one positive solution, quasilinear elliptic equations, principal eigenvalue, order interval, lower solutions, nonlinear elliptic equations, imbedding theorem, nonnegative solution, maximal solution, minimal solution Key Phrases - Capitalized Phrases (CAPs): (learn more)
Using Lemma New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 10
books:
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- Partial Differential Equations (Lectures in Applied Mathematics) by L. Bers in Back Matter
- Methods for Analysis of Nonlinear Elliptic Boundary Value Problems (Translations of Mathematical Monographs) by I. V. Skrypnik in Back Matter
- Linear and quasilinear elliptic equations, Volume 46 (Mathematics in Science and Engineering) by Ladyzhenskaya in Back Matter
- Monotone Operators in Banach Space and Nonlinear Partial Differential Equations (Mathematical Surveys and Monographs) by R. E. Showalter in Back Matter
- An Introduction to Maximum Principles and Symmetry in Elliptic Problems (Cambridge Tracts in Mathematics) by L. E. Fraenkel in Back Matter
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