Liouville-type theorems for a quasilinear elliptic equation of the Hénon-type

the investigation of the relationship between type a and type b personalities and quality of translation

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Liouville-type theorems for stable and finite Morse index solutions of a quasi-linear elliptic equation

We establish Liouville-type theorems for stable and finite Morse index weak solutions of −∆pu = f(x)F (u) in R . For a general non-linearity F ∈ C(R) and f(x) = |x|, we prove such theorems in dimensions N ≤ 4(p+α) p−1 +p, for bounded radial stable solutions. Then, we give some point-wise estimates for not necessarily bounded solutions. Also, similar theorems will be proved for both radial finit...

Liouville Type Theorems for Conformal Gaussian Curvature Equation

In this note, we study Liouville type theorem for conformal Gaussian curvature equation (also called the mean field equation) −∆u = K(x)e, in R where K(x) is a smooth function on R. When K(x) = K(x1) is a signchanging smooth function in the real line R, we have a non-existence result for the finite total curvature solutions. When K is monotone non-decreasing along every ray starting at origin, ...

Liouville type theorems and Harnack type inequalities for semilinear 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...