On Finding Multiple Solutions to a Singularly Perturbed Neumann Problem
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...
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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 ...
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We consider the problem " 2 u ? u + f (u) = 0 in u > 0 in ; @u @ = 0 on @; where is a bounded smooth domain in R N , " > 0 is a small parameter and f is a superlinear, subcritical nonlinearity. It is known that this equation possesses boundary spike solutions such that the spike concentrates, as " approaches zero, at a critical point of the mean curvature function H(P); P 2 @. It is also known ...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2012
ISSN: 1064-8275,1095-7197
DOI: 10.1137/100810411