Nodal solutions of fourth-order Kirchhoff equations with critical growth
in $\R^N$
Abstract
In this paper, we consider the following fourth-order elliptic equations
of Kirchhoff type with critical growth in $\R^N$:
$$ \Delta^2
u-\left(1+b\int_{\R^N}
|\nabla u|^2
dx\right)\Delta u+V(x)u
=\lambda
f(u)+|u|^{2^{**}-2}u, \quad
x\in\R^N, $$ where
$\Delta^2 u$ is the biharmonic operator,
$2^{**}=2N/(N-4)$ is the critical Sobolev exponent with
$N\ge 5$, $b$ and $\lambda$ are two
positive parameters, and $V(x)$ is the potential. By using a main tool
of constrained minimization in Nehari manifold, we establish sufficient
conditions for the existence result of nodal (that is, sign-changing)
solutions.
