Some Liouville theorems for Hénon type elliptic equations

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 theorems on some indefinite equations

In this note, we present some Liouville type theorems about the nonnegative solutions to some indefinite elliptic equations.

Liouville type theorems and Harnack type inequalities for semilinear elliptic equations

Some Remarks on Liouville Type Theorems

The goal of this note is to present elementary proofs of statements related to the Liouville theorem.

Liouville-type theorems and decay estimates for solutions to higher order elliptic equations

Liouville-type theorems are powerful tools in partial differential equations. Boundedness assumption of solutions are often imposed in deriving such Liouville-type theorems. In this paper, we establish some Liouville-type theorems without the boundedness assumption of nonnegative solutions to certain classes of elliptic equations and systems. Using a rescaling technique and doubling lemma devel...