Vakulenko, A. F. Multidimensional Hardy inequalities and the absence of positive eigenvalues for the Schrödinger operator with complex potential. (Russian. English summary) Zbl 0557.35023 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 138, 33-34 (1984). Summary: Using the following estimate \[ \int_{{\mathbb{R}}^ n}| x|^{2p+2}\quad | (\Delta \phi +\phi)|^ 2\quad dx\geq C(p)\int_{{\mathbb{R}}^ n}| x|^{2p}\quad | \phi |^ 2\quad dx \] with C(p)\(\to \infty\) as \(p\to \infty\), we prove the absence of an \(L_ 2\)-solution of \(1/2-\Delta \phi +\vartheta\phi=\phi\) with \(|\vartheta(x)| \leq C(1+| x|)^{-1-\epsilon}\). Cited in 3 Reviews MSC: 35J10 Schrödinger operator, Schrödinger equation 35P15 Estimates of eigenvalues in context of PDEs 35Q99 Partial differential equations of mathematical physics and other areas of application Keywords:multidimensional Hardy inequalities; absence of positive; eigenvalues; Schrödinger operator; complex potential PDFBibTeX XMLCite \textit{A. F. Vakulenko}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 138, 33--34 (1984; Zbl 0557.35023) Full Text: EuDML