Singularly perturbed Neumann problems with potentials
نویسندگان
چکیده
منابع مشابه
Singularly perturbed Neumann problems with potentials
Such a problem was intensively studied in several works. For example, Ni & Takagi, in [11, 12], show that, for ε sufficiently small, there exists a solution uε of (2) which concentrates in a point Qε ∈ ∂Ω andH(Qε) → max∂ΩH , here H denotes the mean curvature of ∂Ω. Moreover in [10], using the LiapunovSchmidt reduction, Li constructs solutions with single peak and multi-peaks on ∂Ω located near ...
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where Ø is a smooth bounded domain of R with external normal ν, N ≥ 3, 1 < p < (N + 2)/(N − 2), J : R → R and V : R → R are C functions. In [5], the first author, extending the classical results by Ni and Takagi, in [3, 4], proved that there exist solutions of (1) that concentrate at maximum and minimum points of a suitable auxiliary function defined on the boundary ∂Ø and depending only on J a...
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We consider the following singularly perturbed semilinear elliptic problem: 2 u ? u + u p = 0 in ; u > 0 in and @u @ = 0 on @; where is a bounded smooth domain in R N , > 0 is a small constant and p is a sub-critical exponent. Let J u] := R (2 2 jruj 2 + 1 2 u 2 ? 1 p+1 u p+1)dx be its energy functional, where u 2 H 1 ((). Ni and Takagi ((15], 16]) proved that for a single boundary spike soluti...
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ژورنال
عنوان ژورنال: Topological Methods in Nonlinear Analysis
سال: 2004
ISSN: 1230-3429
DOI: 10.12775/tmna.2004.013