Solutions of fully nonlinear nonlocal systems
نویسندگان
چکیده
منابع مشابه
Perron’s method for nonlocal fully nonlinear equations
This paper is concerned with existence of viscosity solutions of non-translation invariant nonlocal fully nonlinear equations. We construct a discontinuous viscosity solution of such nonlocal equation by Perron’s method. If the equation is uniformly elliptic, we prove the discontinuous viscosity solution is Hölder continuous and thus it is a viscosity solution.
متن کاملSmooth Solutions to a Class of Nonlocal Fully Nonlinear Elliptic Equations
We show that a certain class of fully nonlinear nonlocal equations have smooth solutions as long as the right-hand side is nice and the boundary datum is bounded. To this end we follow the classical strategy. We first show that solutions are Cσ+α continuous, then develop a bootstrap argument robust enough for operators that may depend on the solution and its σ-derivatives.
متن کاملSolitons in nonlocal nonlinear media: exact solutions.
We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties of these solitons and show their stability.
متن کاملRotating soliton solutions in nonlocal nonlinear media.
We discuss generic properties of rotating nonlinear wave solutions, the so called azimuthons, in nonlocal media. Variational methods allow us to derive approximative values for the rotating frequency, which is shown to depend crucially on the nonlocal response function. Further on, we link families of azimuthons to internal modes of classical non-rotating stationary solutions, namely vortex and...
متن کاملNonlocal feedback in nonlinear systems
A shifted or misaligned feedback loop gives rise to a two-point nonlocality that is the spatial analog of a temporal delay. Important consequences of this nonlocal coupling have been found both in diffusive and in diffractive systems, and include convective instabilities, independent tuning of phase and group velocities, as well as amplification, chirping and even splitting of localized perturb...
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 Mathematical Analysis and Applications
سال: 2017
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2017.01.070