In this paper we study the Lane-Emden-Fowler equation (P)(epsilon) {(Delta)u+vertical bar u vertical bar(q-2) u = 0 in D-epsilon,D- u = 0 on partial derivative D-epsilon. Here D-c = D {x epsilon D : dist (x, Gamma(l) ) <= epsilon }, D is a smooth bounded domain in R-N, Gamma(l) is an l-dimensional closed manifold such that Gamma l subset of D with 1 <= l <= N - 3 and q = 2(N - l)/ N-l-2. We prove that, under some symmetry assumptions, the number of sign changing solutions to (P)(epsilon), increases as goes to zero.
SUPERCRITICAL PROBLEMS IN DOMAINS WITH THIN TOROIDAL HOLES / S., Kim; Pistoia, Angela. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 34:11(2014), pp. 4671-4688. [10.3934/dcds.2014.34.4671]
SUPERCRITICAL PROBLEMS IN DOMAINS WITH THIN TOROIDAL HOLES
PISTOIA, Angela
2014
Abstract
In this paper we study the Lane-Emden-Fowler equation (P)(epsilon) {(Delta)u+vertical bar u vertical bar(q-2) u = 0 in D-epsilon,D- u = 0 on partial derivative D-epsilon. Here D-c = D {x epsilon D : dist (x, Gamma(l) ) <= epsilon }, D is a smooth bounded domain in R-N, Gamma(l) is an l-dimensional closed manifold such that Gamma l subset of D with 1 <= l <= N - 3 and q = 2(N - l)/ N-l-2. We prove that, under some symmetry assumptions, the number of sign changing solutions to (P)(epsilon), increases as goes to zero.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.