Nonexistence of nonconstant global minimizers with limit at ∞ of semilinear elliptic equations in all of R^N

2009/06/08 by Villegas, Salvador
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0906.1440

Abstract

We prove nonexistence of nonconstant global minimizers with limit at infinity of the semilinear elliptic equation -Δu=f(u) in the whole R^N, where f∈ C¹(R) is a general nonlinearity and N≥ 1 is any dimension. As a corollary of this result, we establish nonexistence of nonconstant bounded radial global minimizers of the previous equation.

Related

• Nonexistence result for a semilinear elliptic problem
• Regularity of minimizers of semilinear elliptic problems up to dimension four
• Semilinear elliptic problems in ℝ^N: the interplay between the potential and the nonlinear term
• Boundedness of the extremal solutions in dimension 4
• Existence and asymptotic behavior for the ground state of quasilinear elliptic equation