Order Structure and Topological Methods in Nonlinear Partial Differential Equations: Vol. 1: Maximum Principles and Applications
Order Structure and Topological Methods in Nonlinear Partial Differential Equations: Vol. 1: Maximum Principles and Applications
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DOI：
10.1142/5999
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发表时间：
2006-01
期刊：
影响因子：
--
通讯作者：
Yihong Du
中科院分区：
文献类型：
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作者：
Yihong Du
极大值原理导出了偏微分方程的有序结构，已成为非线性分析的重要工具。这本书是第一个两卷，系统地介绍了在某些非线性偏微分方程问题的有序结构的应用。通过使用克林-鲁特曼定理和主特征值，重新审视了极大原理。它的各种版本，如移动平面和滑动平面方法，被应用于当前感兴趣的各种重要问题。上下解法，特别是弱解法，以其最新的形式呈现，具有足够的通用性，以适应广泛的应用。讨论了边界爆破问题及其应用的最新进展，以及在半空间和全空间上的一些新的对称性和Liouville型结果。这里包括的一些结果是第一次发表。
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.