A uniqueness and periodicity result for solutions of elliptic equations in unbounded domains
نویسندگان
چکیده
We proof a uniqueness and periodicity theorem for bounded solutions of uniformly elliptic equations in certain unbounded domains.
منابع مشابه
Non-existence of Positive Solutions of Fully Nonlinear Elliptic Equations in Unbounded Domains
In this paper we consider fully nonlinear elliptic operators of the form F (x, u,Du,D2u). Our aim is to prove that, under suitable assumptions on F , the only nonnegative viscosity super-solution u of F (x, u,Du,D2u) = 0 in an unbounded domain Ω is u ≡ 0. We show that this uniqueness result holds for the class of nonnegative super-solutions u satisfying inf x∈Ω u(x) + 1 dist(x, ∂Ω) = 0, and the...
متن کاملOn the nature of solutions of the difference equation $mathbf{x_{n+1}=x_{n}x_{n-3}-1}$
We investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers. In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.
متن کاملLiouville type results for semilinear elliptic equations in unbounded domains
This paper is devoted to the study of some class of semilinear elliptic equations in the whole space: −aij(x)∂iju(x)− qi(x)∂iu(x) = f(x, u(x)), x ∈ R . The aim is to prove uniqueness of positive bounded solutions Liouville type theorems. Along the way, we establish also various existence results. We first derive a sufficient condition, directly expressed in terms of the coefficients of the line...
متن کاملAsymptotic behavior of solutions of semilinear elliptic equations in unbounded domains: two approaches
In this paper, we study the asymptotic behavior as x1 → +∞ of solutions of semilinear elliptic equations in quarteror half-spaces, for which the value at x1 = 0 is given. We prove the uniqueness and characterize the one-dimensional or constant profile of the solutions at infinity. To do so, we use two different approaches. The first one is a pure PDE approach and it is based on the maximum prin...
متن کاملOn Neumann and oblique derivatives boundary conditions for nonlocal elliptic equations
Inspired by the penalization of the domain approach of Lions & Sznitman, we give a sense to Neumann and oblique derivatives boundary value problems for nonlocal, possibly degenerate elliptic equations. Two different cases are considered: (i) homogeneous Neumann boundary conditions in convex, possibly non-smooth and unbounded domains, and (ii) general oblique derivatives boundary conditions in s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008