Nonlocal scalar field equations: Qualitative properties, asymptotic profiles and local uniqueness of solutions
نویسندگان
چکیده
منابع مشابه
Uniqueness Properties of Solutions to Schrödinger Equations
j=1 ∂u ∂xj (x) = 0, (harmonic functions) in the unit ball {x ∈ R : |x| < 1}. When n = 2, these functions are real parts of holomorphic functions, and so, if they vanish of infinite order at x = 0, they must vanish identically. We call this the strong unique continuation property (s.u.c.p.). The same result holds for n > 2, since harmonic functions are still real analytic in {x ∈ R : |x| < 1}. I...
متن کاملExact solutions of classical scalar field equations
We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wavelike behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term r...
متن کامل: Existence and Uniqueness of Solutions , Asymptotic and Borel Summability Properties
We consider a system of n-th order nonlinear quasilinear partial differential equations of the form ut + P(∂ j x)u + g ( x, t, {∂ xu} ) = 0; u(x, 0) = uI(x) with u ∈ C, for t ∈ (0, T ) and large |x| in a poly-sector S in C (∂ x ≡ ∂ j1 x1∂ j2 x2 ...∂ jd xd and j1 + ... + jd ≤ n). The principal part of the constant coefficient n-th order differential operator P is subject to a cone condition. The...
متن کاملNonlinear Equations for Fractional Laplacians Ii: Existence, Uniqueness, and Qualitative Properties of Solutions
This paper, which is the follow-up to part I, concerns the equation (−Δ)sv + G′(v) = 0 in Rn, with s ∈ (0, 1), where (−Δ)s stands for the fractional Laplacian—the infinitesimal generator of a Lévy process. When n = 1, we prove that there exists a layer solution of the equation (i.e., an increasing solution with limits ±1 at ±∞) if and only if the potential G has only two absolute minima in [−1,...
متن کاملOn qualitative properties and asymptotic behavior of solutions to higher-order nonlinear differential equations
We discuss the asymptotic behavior of solutions to a higher-order Emden–Fowler type equation with constant potential. Several author’s results are presented concerning both positive and oscillatory solutions to equations with regular and singular nonlinearities. We discuss the existence and asymptotic behavior of “blowup” solutions. Results on the asymptotic behavior of oscillating solutions ar...
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: Journal of Differential Equations
سال: 2019
ISSN: 0022-0396
DOI: 10.1016/j.jde.2018.11.023