Order structure and topological methods in nonlinear partial differential equations maximum..非线性偏微分方程的阶结构与拓扑方法，第1卷：极大值原理与应用
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作者： Yihong Du著
出 版 社：
出版时间： 2006-1-1字数：版次：页数： 190印刷时间： 2006/01/01开本： 16开印次：纸张： 胶版纸I S B N ： 9789812566249包装： 精装内容简介
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 haft and entire spaces. Some of the results included here are published for the first time.
目录
Preface
1. Krein-Rutman Theorem and the Principal Eigenvalue
2. Maximum Principles Revisited
2.1 Equivalent forms of the maximum principle
2.2 Maximum principle in w2'N
3. The Moving Plane Method
3.1 Symmetry over bounded domains
3.2 Symmetry over the entire space
3.3 Positivity of nonnegative solutions
4. The Method of Upper and Lower Solutions
4.1 Classical upper and lower solutions
4.2 Weak upper and lower solutions
5. The Logistic Equation
5.1 The classical case
5.2 The degenerate logistic equation
5.3 Perturbation and profile of solutions
6. Boundary Blow-Up Problems
6.1 The Keller-Osserman result and its generalizations
6.2 Blow-up rate and uniqueness
6.3 Logistic type equations with weights Maximum Principles and Applications
7. Symmetry and Liouville Type Results over Half and Entire Spaces
7.1 Symmetry in a half space without strong maximum principle
7.2 Uniqueness results of logistic type equations over RN
7.3 Partial symmetry in the entire space
7.4 Some Liouville type results
Appendix A Basic Theory of Elliptic Equations
A.1 Schauder theory for elliptic equations
A.2 Sobolev spaces
A.3 Weak solutions of elliptic equations
A.4 Lp theory of elliptic equations
A.5 Maximum principles for elliptic equations
A.5.1 The classical maximum principles
A.5.2 Maximum principles and Harnack inequality for weak solutions
A.5.3 Maximum principles and Harnack inequality for strong solutions
Bibliography
Index
