We study the asymptotic behaviour as p -> infinity of the nodal radial solutions u(p) of the problem {-Delta u = vertical bar u vertical bar(p-1)u in Omega u = 0 on partial derivative Omega, where Omega is an annulus in R-N, N >= 2. We also analyze the spectrum of the linearized operator associated to u(p) in the case when u(p) has only two nodal regions. In particular, we prove that the Morse index of u(p) tends to infinity as p goes to infinity.
ASYMPTOTIC BEHAVIOUR OF SIGN CHANGING RADIAL SOLUTIONS OF LANE EMDEN PROBLEMS IN THE ANNULUS / Pacella, Filomena; Dora, Salazar. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 7:4(2014), pp. 793-805. [10.3934/dcdss.2014.7.793]
ASYMPTOTIC BEHAVIOUR OF SIGN CHANGING RADIAL SOLUTIONS OF LANE EMDEN PROBLEMS IN THE ANNULUS
PACELLA, Filomena;
2014
Abstract
We study the asymptotic behaviour as p -> infinity of the nodal radial solutions u(p) of the problem {-Delta u = vertical bar u vertical bar(p-1)u in Omega u = 0 on partial derivative Omega, where Omega is an annulus in R-N, N >= 2. We also analyze the spectrum of the linearized operator associated to u(p) in the case when u(p) has only two nodal regions. In particular, we prove that the Morse index of u(p) tends to infinity as p goes to infinity.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
