Numerical solution of a critical Sobolev exponent problem with weight on 𝕊3

Abstract

In this paper, we prove the existence of a positive solution for elliptic nonlinear partial differential equation with weight involving a critical exponent of Sobolev imbedding on $ \mathbb {S}^{3} $ . Moreover, we discuss numerically the influence of the weight on the radius of the domain for which the given PDE has a positive solution.

Keywords

• critical sobolev exponent
• variational methods
• runge–kutta method