Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on $R^n$

Paolo Caldiroli

doi:10.3934/cpaa.2014.13.811

Article Contents

2014, Volume 13, Issue 2: 811-821. Doi: 10.3934/cpaa.2014.13.811

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Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on $R^n$

Paolo Caldiroli^1,

1.
Dipartimento di Matematica, Università di Torino, via Carlo Alberto, 10-10123 Torino

Received: March 31, 2013

Revised: June 30, 2013

Published: February 2014

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Abstract

We prove existence of extremal functions for some Rellich-Sobolev type inequalities involving the $L^2$ norm of the Laplacian as a leading term and the $L^2$ norm of the gradient, weighted with a Hardy potential. Moreover we exhibit a breaking symmetry phenomenon when the nonlinearity has a growth close to the critical one and the singular potential increases in strength.

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Mathematics Subject Classification: 26D10, 47F05.

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