Liouville type theorems for elliptic systems involving gradient terms

New conditions on ground state solutions for Hamiltonian elliptic systems with gradient terms

This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...

Liouville-Type Theorems for Some Integral Systems

/2 ( ) ( ) u u        where  is the Fourier transformation and  its inverse. The question is to determine for which values of the exponents pi and qi the only nonnegative solution (u, v) of (1) and (2) is trivial, i.e., (u; v) = (0, 0). When 2   , is the case of the Emden-Fowler equation 0 , 0     u u u k in N  (5) When ) 3 )( 2 /( ) 2 ( 1      N N N k , it has been prove...

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...

new conditions on ground state solutions for hamiltonian elliptic systems with gradient terms

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...

Liouville type theorems and Harnack type inequalities for semilinear elliptic equations