Liouville-Type Theorems for Some Integral Systems

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...

Some Remarks on Liouville Type Theorems

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

Some Liouville theorems and applications

We give exposition of a Liouville theorem established in [6] which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof of the classical Liouville theorem for harmonic functions. Applications of the Liouville theorem, as well as that of earlier ones in [5], can be found in [6, 7] an...

Some Fixed Point Theorems for Weakly Compatible Multivalued Mappings Satisfying Some General Contractive Conditions of Integral Type

Liouville theorems on some indefinite equations

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