On a class of critical <i>N</i>-Laplacian problems

Abstract We establish some existence results for a class of critical $N$ -Laplacian problems in bounded domain $\mathbb {R}^{N}$ . In the absence suitable direct sum decomposition underlying Sobolev space to which classical linking theorem can be applied, we use an abstract based on {Z}_2$ -cohomological index obtain non-trivial point.