On the behaviour of the solutions for a class of nonlinear elliptic problems in exterior domains

Riccardo Molle; Donato Passaseo

doi:10.3934/dcds.1998.4.445

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1998, Volume 4, Issue 3: 445-454. Doi: 10.3934/dcds.1998.4.445

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On the behaviour of the solutions for a class of nonlinear elliptic problems in exterior domains

Riccardo Molle^1, and
Donato Passaseo^2,

1.
Dipartimento di Matematica, Università di Pisa, Via Buonarroti, 2, 56127 PISA
2.
Dipartimento di Matematica, Università di Pisa, Via Buonarroti, 2 56127 - PISA

Received: January 31, 1997

Revised: June 30, 1997

Published: June 1998

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Abstract

We state a result concerning the limit of a class of minimization problems. This result is applied to describe the asymptotic behaviour of the solutions of an elliptic Dirichlet problem in exterior domains $\Omega$ of $\mathbb{R}^N$, when $\mathbb{R}^N$ \ $Omega$ becomes larger and larger.

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Mathematics Subject Classification: 35J65, 35J20.

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