Radially symmetric internal layers in a semilinear elliptic system
نویسندگان
چکیده
منابع مشابه
Radially Symmetric Internal Layers for an Inhibitory System
We are concerned with an activator-inhibitor system on an n-dimensional ball such that the inhibitor is activated by an activator as well as the spatial average of its inhibitor. We analyze the existence of the radially symmetric solutions and the occurrence of Hopf bifurcation in the interfacial problem as the bifurcation parameters vary. Mathematics Subject Classification: 35R35, 35B32, 35B25...
متن کاملRadially Symmetric Solutions of a Nonlinear Elliptic Equation
We investigate the existence and asymptotic behavior of positive, radially symmetric singular solutions of w′′ N − 1 /r w′ − |w|p−1w 0, r > 0. We focus on the parameter regime N > 2 and 1 < p < N/ N − 2 where the equation has the closed form, positive singular solution w1 4 − 2 N − 2 p − 1 / p − 1 2 1/ p−1 r−2/ p−1 , r > 0. Our advance is to develop a technique to efficiently classify the behav...
متن کاملRadially Symmetric Solutions for a Class ofCritical Exponent Elliptic Problems in RN
We give a method for obtaining radially symmetric solutions for the critical exponent problem ?u + a(x)u = u q + u 2 ?1 in R N u > 0 and R R N jruj 2 < 1 where, outside a ball centered at the origin, the non-negative function a is bounded from below by a positive constant ao > 0. We remark that, diierently from the literature, we do not require any conditions on a at innnity.
متن کاملAsymptotic Profile of a Radially Symmetric Solution with Transition Layers for an Unbalanced Bistable Equation
In this article, we consider the semilinear elliptic problem −ε∆u = h(|x|)(u− a(|x|))(1− u) in B1(0) with the Neumann boundary condition. The function a is a C1 function satisfying |a(x)| < 1 for x ∈ [0, 1] and a′(0) = 0. In particular we consider the case a(r) = 0 on some interval I ⊂ [0, 1]. The function h is a positive C1 function satisfying h′(0) = 0. We investigate an asymptotic profile of...
متن کاملExistence and uniqueness of solutions for a semilinear elliptic system
We consider the existence, the nonexistence, and the uniqueness of solutions of some special systems of nonlinear elliptic equations with boundary conditions. In a particular case, the system reduces to the homogeneous Dirichlet problem for the biharmonic equation ∆ 2 u = |u| p in a ball with p > 0.
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: 1995
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1995-1303116-3