 
Summary: Positivity 5: 359382, 2001.
© 2001 Kluwer Academic Publishers. Printed in the Netherlands.
359
Positivity and Negativity of Solutions to a
Schrödinger Equation in RN
BÉNÉDICTE ALZIARY1,2
, JACQUELINE FLECKINGERPELLÉ1,3,
and
PETER TAKÁC4,
1CEREMATH and UMR MIP, Université des Sciences Sociales, 21 Allee de Brienne, F31042
Toulouse Cedex, France, 2Email: alziary@univtlse1.fr and 3Email: jfleck@univtlse1.fr
4Fachbereich Mathematik, Universität Rostock, Universitätsplatz 1, D18055 Rostock, Germany.
Email: peter.takac@mathematik.unirostock.de
(Received 13 April 1999; accepted 6 March 2000)
Abstract. Weak L2(RN )solutions u of the Schrödinger equation,  u + q(x)u  u = f (x)
in L2(RN ), are represented by a Fourier series using spherical harmonics in order to prove the
following strong maximum and antimaximum principles in RN (N 2): Let 1 denote the positive
eigenfunction associated with the principal eigenvalue 1 of the Schrödinger operator A =  +
q(x)· in L2(RN ). Assume that the potential q(x) is radially symmetric and grows fast enough near
infinity, and f is a `sufficiently smooth' perturbation of a radially symmetric function, f 0 and
