Nodal solutions for some singularly perturbed Dirichlet problems
نویسندگان
چکیده
منابع مشابه
Concentration of solutions for some singularly perturbed Neumann problems
In these notes we describe some methods for studying the asymptotic behavior of solutions to a class of singularly perturbed elliptic problems. We present first the case of concentration at single points, and then at sets of positive dimension.
متن کاملMultiple Boundary Peak Solutions for Some Singularly Perturbed Neumann Problems
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 ...
متن کاملSymmetry of Nodal Solutions for Singularly Perturbed Elliptic Problems on a Ball
In [40], it was shown that the following singularly perturbed Dirichlet problem 2∆u− u+ |u|p−1u = 0, in Ω, u = 0 on ∂Ω has a nodal solution u which has the least energy among all nodal solutions. Moreover, it is shown that u has exactly one local maximum point P 1 with a positive value and one local minimum point P 2 with a negative value and, as → 0, φ(P 1 , P 2 ) → max (P1,P2)∈Ω×Ω φ(P1, P2), ...
متن کاملHigher Order Energy Expansions for Some Singularly Perturbed Neumann Problems
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...
متن کاملFem for Singularly Perturbed Problems
We consider the numerical approximation of singularly perturbed elliptic boundary value problems over non-smooth domains. We use a decomposition of the solution that contains a smooth part, a corner layer part and a boundary layer part. Explicit guidelines for choosing mesh-degree combinations are given that yield nite element spaces with robust approximation properties. In particular, we const...
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: Transactions of the American Mathematical Society
سال: 2011
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2011-05221-9