Somayeh Khademloo - Department of Basic Sciences, Babol Noushirvani University of Technology, ۴۷۱۴۸-۷۱۱۶۷, Babol, Iran.
Saeed Khanjany Ghazi - Department of Basic Sciences, Babol Noushirvani University of Technology, ۴۷۱۴۸-۷۱۱۶۷, Babol, Iran.

In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.

Variational methods, Nehari manifold, Dirichlet boundary condition, Critical Sobolev exponent