Abstract
In this work, we are interested in a nonlinear PDE of the form: -Delta u = K(x)un+2/n-2, u > 0 on Omega and u = 0 on partial derivative Omega, where n >= 3 and Omega is a regular bounded domain of R-n. Following the results of [K. Sharaf, Appl. Anal. 96(2017), No. 9, 1466-1482] and [K. Sharaf, On an elliptic boundary value problem with critical exponent, Turk. J. Math., to appear], we provide a full description of the loss of compactness of the problem and we establish a general index account formula of existence result, when the flatness order of the function K at any of its critical points lies in (1, infinity).