We consider the boundary value problem Delta u + u(P) = 0 in a bounded, smooth domain Omega in R(2) with homogeneous Dirichlet boundary condition and p a large exponent. We find topological conditions on Omega which ensure the existence of a positive solution up concentrating at exactly m points as p -> infinity. In particular, for a nonsimply connected domain such a solution exists for any given m >= 1. (c) 2006 Elsevier Inc. All rights reserved.
Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent / Pierpaolo, Esposito; Monica, Musso; Pistoia, Angela. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 227:1(2006), pp. 29-68. [10.1016/j.jde.2006.01.023]
Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent
PISTOIA, Angela
2006
Abstract
We consider the boundary value problem Delta u + u(P) = 0 in a bounded, smooth domain Omega in R(2) with homogeneous Dirichlet boundary condition and p a large exponent. We find topological conditions on Omega which ensure the existence of a positive solution up concentrating at exactly m points as p -> infinity. In particular, for a nonsimply connected domain such a solution exists for any given m >= 1. (c) 2006 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
