“…The novelty of this paper is as follows: in all the aforementioned papers, limit index theory [16] was applied, but the (PS) * c condition, which is described in Definition 2, should be considered. However, in the papers of Chung [15,20], Chems Eddine [21], Liang and Shi [17], Liang and Zhang [14,18,19], Li and Song [22], Sun and Bai et al [23], and Song and Shi [24], with the concentration-compactness principle [25], the boundness of the (PS)…”