Multiple positive solutions for a singularly perturbed Dirichlet problem in "geometrically trivial" domains
نویسندگان
چکیده
منابع مشابه
On Finding Multiple Solutions to a Singularly Perturbed Neumann Problem
In this paper, in order to numerically solve for multiple positive solutions to a singularly perturbed Neumann boundary value problem in mathematical biology and other applications, a local minimax method is modified with new local mesh refinement and other strategies. Algorithm convergence and other related properties are verified. Motivated by the numerical algorithm and convinced by the nume...
متن کاملThe Dirichlet Problem for Singularly Perturbed Elliptic Equations
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. I...
متن کاملMultipeak Solutions for a Singularly Perturbed Neumann Problem
Problem (1.1) appears in applied mathematics. See for example [13, 14] and the references therein. For the interesting link between this problem and the modelling of activator-inhibitor systems, the authors can refer to [11]. In [13, 14], Ni and Takagi prove that the least energy solution of (1.1) has exactly one local maximum point xε which lies in ∂Ω, and xε tends to a point x0 which attains ...
متن کاملTriple Junction Solutions for a Singularly Perturbed Neumann Problem
We consider the following singularly perturbed Neumann problem ε∆u− u + u = 0 , u > 0 in Ω, ∂u ∂ν = 0 on ∂Ω, where p > 1 and Ω is a smooth and bounded domain in R. We construct a class of solutions which consist of large number of spikes concentrating on three line segments with a common endpoint which intersect ∂Ω orthogonally .
متن کاملA Singularly Perturbed Linear Eigenvalue Problem in C1 Domains
where ν is the outward unit normal vector on ∂Ω; ν exists a.e. for Lipschitz domains. The goal of this paper is to understand the asymptotic behavior of Λ(γ) as γ → ∞ when ∂Ω ∈ C1. Since Λ(γ) → ∞ when γ → ∞, (2) can be viewed as a singularly perturbed linear eigenvalue problem. The asymptotic behavior of Λ(γ) was first studied by Lacey, Ockendon and Sabina in [3], where they investigated some r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topological Methods in Nonlinear Analysis
سال: 2002
ISSN: 1230-3429
DOI: 10.12775/tmna.2002.004