The Existence Of Solutions To Two Types Of Kirchhoff-type Equations

This paper mainly studies two Kirchhoff type equations.Firstly,we are concerned with the following Kirchhoff equation:where N?3,(a>1,??0 is a parameter,and f(t) is asymptotically linear at infinity.By using variational methods,we obtain the existence of nontrivial solutions under appropriate assumptions on K(x).A cut-off functional is utilized to obtain the bounded Palais-Smale sequences.Secondly,we consider the other Kirchhoff equation:The sign of the potential of the equation is uncertain.By using variational methods,we ob-tain the existence of multiple nontrivial solutions under appropriate assumptions on f(x,u).