An alternative approach to critical PDEs

Abstract

In this article, we use an alternative method to prove the existence of an infinite sequence of distinct non-radial nodal G-invariant solutions for critical nonlinear elliptic problems defined in the whole the Euclidean space. Our proof is via approximation of the problem on symmetric bounded domains. The base model problem of interest originating from Physics is stated below: $$ -\Delta u = |u|^{\frac{4}{n-2}}u ,\quad u\in C^2(\mathbb{R}^n), \quad n\geq3. $$

Keywords

• Laplacian
• non-radial solution
• critical exponent