Liouville type theorem associated with the wave equation
نویسندگان
چکیده
منابع مشابه
A Birkhoff–Lewis type theorem for the nonlinear wave equation
We give an extension of the celebrated Birkhoff–Lewis theorem to the nonlinear wave equation. Accordingly we find infinitely many periodic orbits with longer and longer minimal periods accumulating at the origin, which is an elliptic equilibrium of the associated infinite dimensional Hamiltonian system.
متن کاملA Liouville-type theorem for Schrödinger operators
In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a symmetric critical operator P1, such that a nonzero subsolution of a symmetric nonnegative operator P0 is a ground state. Particularly, if Pj := −∆ + Vj , for j = 0, 1, are two nonnegative Schrödinger operators defined on Ω ⊆ R such that P1 is critical in Ω with a ground state φ, the function ψ 0 is a...
متن کاملA Liouville-type theorem and the decay of radial solutions of a semilinear heat equation
We consider the semilinear parabolic equation ut = ∆u+ up on RN , where the power nonlinearity is subcritical. We first address the question of existence of entire solutions, that is, solutions defined for all x ∈ RN and t ∈ R. Our main result asserts that there are no positive radially symmetric bounded entire solutions. Then we consider radial solutions of the Cauchy problem. We show that if ...
متن کاملA Liouville Type Theorem for Special Lagrangian Equations with Constraints
We derive a Liouville type result for special Lagrangian equations with certain “convexity” and restricted linear growth assumptions on the solutions.
متن کاملOn a Liouville-type equation with sign-changing weight
In this paper we study the existence, nonexistence and multiplicity of non-negative solutions for the family of problems −∆u = λ (a(x)e + f(x, u)), u ∈ H 0 (Ω) where Ω is a bounded domain in R2 and λ > 0 is a parameter. The coefficient a(x) is allowed to change sign. The techniques used in the proofs are a combination of upper and lower solutions, the TrudingerMoser inequality and variational m...
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: Mathematical Journal of Ibaraki University
سال: 2011
ISSN: 1883-4353,1343-3636
DOI: 10.5036/mjiu.43.51