 01142 Michael Heid, HansPeter Heinz, Tobias Weth
 Nonlinear Eigenvalue Problems Of Schrödinger Type Admitting
Eigenfunctions With Given Spectral Characteristics
(78K, LaTeX 2e)
Apr 11, 01

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. The following work is an extension of our recent paper \cite{HdHz99}. We
still deal with nonlinear eigenvalue problems of the form
\begin{eqspeclab}{*}
A_0 y + B(y) y = \lambda y
\end{eqspeclab}
in a real Hilbert space $\cH$ with a semibounded selfadjoint operator
$A_0$, while for every y from a dense subspace $X$ of $\cH$, $B(y)$ is a
symmetric operator. The lefthand side is assumed to be related to a certain
auxiliary functional $\psi$, and the associated linear problems
\begin{eqspeclab}{**}
A_0 v + B(y) v = \mu v
\end{eqspeclab}
are supposed to have nonempty discrete spectrum $\: (y \in X)$.We
reformulate and generalize the topological method presented by the authors in
$\cite{HdHz99}$ to construct solutions of (*) on a sphere $S_R := \{ y \in X
 \: \y\_{\cH} = R\}$ whose $\psi$value is the $n$th \ls level of $\psi
_{S_R}$ and whose corresponding eigenvalue is the $n$th eigenvalue of the
associated linear problem (**), where $R > 0$ and $n \in \nz$ are given. In
applications, the eigenfunctions thus found share any geometric property
enjoyed by an $n$th eigenfunction of a linear problem of the form (**). We
discuss applications to elliptic partial differential equations with radial
symmetry.
 Files:
01142.tex