By the concentration-compactness principle the author proves the existence of a second entire solution to the semilinear elliptic equation
, if , , and for large in addition to the known positive solution given e.g. by P. L. Lions [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 1, 109-145 (1984; Zbl 0541.49009) and 223-283 (1984)] or E. S. Noussair and C. A. Swanson [Hiroshima Math. J. 15, 127-140 (1985; Zbl 0575.35025)]. Compare also the totally different technique of E. S. Noussair [Bull. Lond. Math. Soc. 19, 443-448 (1987; Zbl 0633.35025)] where the existence of a second positive solution for the slightly different equation is proved.