On spectrum of boundary value problem for biharmonic equation in half-space (Q2782064)

The authors study the spectrum of a nonselfadjoint boundary value problem for biharmonic equation in half-space. The main result of the paper is as follows. Let \(\rho(T)\neq \emptyset \) and NEWLINE\[NEWLINE \alpha_{jk}(x) = o(x),\quad \|x\|\to \infty NEWLINE\]NEWLINE for all \(j=0,1\), \(k=0,1,2,3\). Then (a) \(\sigma_{\text{ess}}(T) = [0,\infty)\); (b) \(\sigma(T)\backslash[0,\infty)=\sigma_{p,0}\), where \(\sigma(*)\), \(\sigma_p(*)\), \(\sigma_{\text{ess}}(*)\) and \(\rho(*)\) are the spectrum, the point spectrum, the essential spectrum and the resolvent set of the operator~\((*)\).NEWLINENEWLINENEWLINEThe main result is obtained in terms of the approach associated with singular perturbations of selfadjoint operators.