Positive solution for a superlinear Kirchhoff type problem with a parameter

This paper is devoted to a nonlinear Kirchhoff type problem depending on a real function and a nonnegative parameter on a smooth bounded domain of RNRN, N≥2N≥2. We show that if the nonlinearity is subcritical and superlinear at zero and infinity, then there exists a positive value such that the Kirchhoff type problem has at least one positive solution for any value of the parameter less than the positive value. The main tools are variational methods, critical point theory and iterative techniques.