Concentration-compactness principle at infinity and semilinear elliptic equations involving critical and subcritical Sobolev exponents (Q1902318)

In this interesting paper, the author formulates and proves his concentration-compactness principle at \(\infty\), which can be used instead of the first variational principle of \textit{P. L. Lions} [Ann. Inst. Henri Poincaré, Anal. Non Lineaire 1, 109-145 (1984; Zbl 0541.49009) and ibid., 223-283 (1984; Zbl 0704.49004)]. Then he gives applications, rich in substance, to some nonlinear elliptic equations: First, to an equation, which originates in differential geometry (the Yamabe problem), using a mountain pass theorem. Second, he reproves known existence theorems for certain equations. In doing so, his approach seems to be simpler and under slightly weaker conditions.