(untitled) (Journal of Partial Differential Equations, 2017)
This paper is concerned with the existence of nontrivial solutions for the following fourth-order equations of Kirchhoff type equation*casesΔ^2u-(a+b_R ^N | ablau|^2dx)Δu+λ V(x)u=f(x,u),xR^N , uH^2(R ^N),casesequation* where a,b are positive constants, λ ≥ 1 is a parameter, and the nonlinearity f is either superlinear or sublinear at infinity in u. With the help of the variational methods, we obtain the existence and multiplicity results in the working spaces.