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The Dirichlet problem for singularly perturbed elliptic equations
Author(s) -
Li Yanyan,
Nirenberg Louis
Publication year - 1998
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199811/12)51:11/12<1445::aid-cpa9>3.0.co;2-z
Subject(s) - nirenberg and matthaei experiment , mathematics , dirichlet distribution , citation , computational science and engineering , library science , algebra over a field , combinatorics , computer science , pure mathematics , mathematical analysis , boundary value problem
There has been much work on various singularly perturbed partial differential equations or systems. Such equations or systems depend on some small parameters ε > 0, solutions denoted as uε. There are at least two types of questions being investigated. The first type is to study possible behavior of uε as ε tends to zero. The second is to actually construct, by various methods, such solutions. In this paper we mainly present some results of the second type. We will study some specific singularly perturbed partial differential equations. However, the methods we used are useful in studying other problems as well. Let Ω ⊂ Rn be a bounded domain with smooth boundary. We consider { −ε2∆ũ+ ũ = ũq , ũ > 0 , in Ω , ũ ∣∣ ∂Ω = 0 , (0.1)