Let M be a smooth k-dimensional closed submanifold of R(N), N >= 2, and let Omega(R) be the open tubular neighborhood of radius 1 of the expanded manifold M(R) := {Rx : x is an element of M}. For R sufficiently large we show the existence of positive multibump solutions to the problem -Delta u + lambda u = f(u) in Omega(R), u = 0 on partial derivative Omega(R). The function f is superlinear and subcritical, and lambda > -lambda(1), where lambda(1) is the first Dirichlet eigenvalue of -Delta in the unit ball in R(N-k).
Self-focusing Multibump Standing Waves in Expanding Waveguides / Nils, Ackermann; Monica, Clapp; Pacella, Filomena. - In: MILAN JOURNAL OF MATHEMATICS. - ISSN 1424-9286. - STAMPA. - 79:1(2011), pp. 221-232. [10.1007/s00032-011-0147-6]
Self-focusing Multibump Standing Waves in Expanding Waveguides
PACELLA, Filomena
2011
Abstract
Let M be a smooth k-dimensional closed submanifold of R(N), N >= 2, and let Omega(R) be the open tubular neighborhood of radius 1 of the expanded manifold M(R) := {Rx : x is an element of M}. For R sufficiently large we show the existence of positive multibump solutions to the problem -Delta u + lambda u = f(u) in Omega(R), u = 0 on partial derivative Omega(R). The function f is superlinear and subcritical, and lambda > -lambda(1), where lambda(1) is the first Dirichlet eigenvalue of -Delta in the unit ball in R(N-k).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
