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.
2006
concentrating solutions; finite-dimensional reduction; green's function; green’s function; large exponent
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/66956
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