Existence of Ground State Solutions for Kirchhoff Problems with Hardy Potential

This study is concerned with the following Kirchhoff problem: -(a + b integral(R3) vertical bar del u vertical bar(2)dx) Delta u - mu/vertical bar x vertical bar(2)u = g(u) in R-3\{0}, (A) where a, b > 0 are constants, mu < 1/4. 1/vertical bar x vertical bar(2) is called the Hardy potential and g : R -> R is a continuous function that satisfies the Berestycki-Lion type condition. Using variational methods, we establish two existence results for problem (A) under different conditions for g. Furthermore, if mu < 0, we prove that the mountain pass level in H-1(R-3) can not be achieved.