Positive solutions to a linearly perturbed critical growth biharmonic problem

Elvise Berchio; Filippo Gazzola

doi:10.3934/dcdss.2011.4.809

Article Contents

2011, Volume 4, Issue 4: 809-823. Doi: 10.3934/dcdss.2011.4.809

This issue Previous Article A remark on Hardy type inequalities with remainder terms Next Article Shape optimization for Monge-Ampère equations via domain derivative

Positive solutions to a linearly perturbed critical growth biharmonic problem

Elvise Berchio^1, and
Filippo Gazzola^1,

1.
Dipartimento di Matematica del Politecnico, Piazza L. da Vinci 32, Milano, 20133

Received: August 31, 2009

Revised: November 30, 2009

Published: July 2011

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Abstract

Existence and nonexistence results for positive solutions to a linearly perturbed critical growth biharmonic problem under Steklov boundary conditions, are determined. Furthermore, by investigating the critical dimensions for this problem, a Sobolev inequality with remainder terms, of both interior and boundary type, is deduced.

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Mathematics Subject Classification: Primary: 35J35, 35J40; Secondary: 35G30.

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