On the Brezis–Nirenberg problem for a Kirchhoff type equation in high dimension

The present paper deals with a parametrized Kirchhoff type problem involving critical nonlinearity in high dimension. Existence, non existence and multiplicity of solutions are obtained under the effect subcritical perturbation by combining variational properties careful analysis fiber maps energy functional associated to problem. particular case pure power is also addressed. Through study Nehari manifolds we extend general wider range parameters.