Quasilinear elliptic systems with critical Sobolev exponents in \(\mathbb {R}^N\)
The paper deals with a quasilinear system involving the \(p\)-Laplacian on \(\mathbb R^N\), the critical Sobolev exponent and a parameter \(\lambda>0\). The existence of a nontrivial weak solution provided \(\lambda\) is sufficiently small is shown. The main technical tools are the verification of the Palais-Smale condition at levels in a specific range and application of the mountain pass theorem.
scientific article; zbMATH DE number 5142208