Classification of stable solutions for non-homogeneous higher-order elliptic PDEs.

Under some assumptions on the nonlinearity , we will study the nonexistence of nontrivial stable solutions or solutions which are stable outside a compact set of [Formula: see text] for the following semilinear higher-order problem: [Formula: see text] with [Formula: see text]. The main methods used are the integral estimates and the Pohozaev identity. Many classes of nonlinearity will be considered; even the sign-changing nonlinearity, which has an adequate subcritical growth at zero as for example [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text].