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arXiv · 1603.05641

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

Francesca Gladiali·Massimo Grossi·Christophe Troestler
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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.

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Francesca Gladiali, Massimo Grossi, Christophe Troestler. 2016-03-17. A non-variational system involving the critical Sobolev exponent. The radial case. https://arxiv.org/abs/1603.05641

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