Some further results on a semilinear equation with concave-convex nonlinearity

Following our previous work [J. Math. Anal. Appl. 295 (2004) 341], we give an exact growth order near zero for positive solutions of a class of elliptic equation and use it to give the existence of multiple solutions with negative energy, multiple positive solutions and sign changing solutions of the considered problem. Even in the particular case, our results extend a previous work by Ambrosetti-Garcia-Peral [J. Funct. Anal. 137 (1996) 219].