Existence Of Solutions For The Kirchhoff Type Equation With A General Nonlinear Term

This dissertation is mainly concerned with the existence and nonexistence results for the Kirchhoff equation with a general nonlinear term where a>0,b?0 are two constants,V:R3?R is a potential function and f:R3?R is a general nonlinear term.Our analysis introduces variational techniques to the analysis of the effect of the nonlinearity,especially those cases when the concentration-compactness principle cannot be applied for obtaining the compactness of the bounded Palais-Smale sequences and a minimizing problem related to the existence of a ground state on the Pohozaev manifold rather than the Nehari manifold associated with the equation.