Liouville type theorems for the system of fractional nonlinear equations in R + n ${R^{n}_{+}}$

Liouville-type theorems for fully nonlinear elliptic equations and systems in half spaces

In [LWZ], we established Liouville-type theorems and decay estimates for solutions of a class of high order elliptic equations and systems without the boundedness assumptions on the solutions. In this paper, we continue our work in [LWZ] to investigate the role of boundedness assumption in proving Liouville-type theorems for fully nonlinear equations. We remove the boundedness assumption of sol...

Existence and Continuation Theorems of Riemann-Liouville Type fractional differential equations

In this paper we study the existence and continuation of solution to the general fractional differential equation (FDE) with Riemann–Liouville derivative. If no confusion appears, we call FDE for brevity. We firstly establish a new local existence theorem. Then, we derive the continuation theorems for the general FDE, which can be regarded as a generalization of the continuation theorems of the...

Further results on Liouville type theorems for some conformally invariant fully nonlinear equations

Liouville type of theorems with weights for the Navier-Stokes equations and the Euler equations

We study Liouville type of theorems for the Navier-Stokes and the Euler equations on R N , N ≥ 2. Specifically, we prove that if a weak solution (v, p) satisfies |v| 2 +|p| ∈ L 1 (0, T ; L 1 (R N , w 1 (x)dx)) and R N p(x, t)w 2 (x)dx ≥ 0 for some weight functions w 1 (x) and w 2 (x), then the solution is trivial, namely v = 0 almost everywhere on R N × (0, T). Similar results hold for the MHD ...

Existence and multiplicity of positive solutions for a coupled system of perturbed nonlinear fractional differential equations

In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.