A non-variational system involving the critical Sobolev exponent. The radial case

TL;DR

This paper investigates a non-variational elliptic system with critical Sobolev exponent, establishing conditions on the coefficient matrix that guarantee solutions bifurcate from the standard bubble in the radial case.

Contribution

It provides new sufficient conditions on the matrix for bifurcation of solutions in a non-variational critical Sobolev system, expanding understanding beyond variational frameworks.

Findings

Identifies conditions on the matrix $(a_{ij})$ for solution bifurcation.

Establishes existence of solutions near the bubble of the critical Sobolev equation.

Focuses on the radial case in $ ext{R}^N$.

Abstract

In this paper we consider the non-variational system $$ \begin{cases} -\Delta u_i = \sum\limits_{j=1}^k a_{ij} u_j^{(N+2)/(N-2)} &\text{in }\mathbb R^N,\newline u_i>0 &\text{in }\mathbb R^N,\newline u_i\in D^{1,2}(\mathbb R^N). \end{cases} $$ and we give some sufficient conditions on the matrix $(a_{ij})_{i,j=1,\dotsc ,k}$ which ensure the existence of solutions bifurcating from the bubble of the critical Sobolev equation.