Let Ω be a bounded smooth domain in R N . Assume that 0 < α < 2 * −1 2 , a > 0, and b > 0. We consider the following Dirichlet problem of Kirchhoff type equationWhere 2 * = +∞ for N = 2, and 2 * = N +2 N −2 for N ≥ 3. Under suitable conditions of h(x, u, ∇u) (see (A), (H 1 ) and (H 2 ) in section 3), we get a priori estimates for positive solutions to problem (0.1). By making use of these estimates and the continuous method, we further get existence results for positive solution to problem (0.1) when 0 < p < 1, or 2α + 1 < p < 2 * . Effects of the term b||∇u|| 2α+1 2 on the solution set of problem (0.1) can be seen from an example given in section 2.

No abstract

No abstract

No abstract