Radial solutions of semilinear elliptic equations with broken symmetry on unbounded domains

Sara Barile; Addolorata Salvatore

doi:10.3934/proc.2013.2013.41

Article Contents

2013, Volume 2013: 41-49. Doi: 10.3934/proc.2013.2013.41 open access

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Radial solutions of semilinear elliptic equations with broken symmetry on unbounded domains

Sara Barile^1, and
Addolorata Salvatore^1,

1.
Dipartimento di Matematica, Università degli Studi di Bari "Aldo Moro", Via E. Orabona 4, 70125 Bari

Received: September 2012

Revised: May 2013

Published: October 2013

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Abstract

We study a superlinear perturbed elliptic problem on $\mathbb R^N$ with rotational symmetry. Using variational and perturbative methods we find infinitely many radial solutions for any growth exponent $p$ of the nonlinearity greater than $2$ and less than $2^*$ if $N \geq 4$ and for any $p$ greater than $3$ and subcritical if $N =3$.

Keywords:

Radial solutions,
variational and perturbative methods,
unbounded domains,
elliptic equations with broken symmetry.

Mathematics Subject Classification: Primary: 35J20; Secondary: 35B38, 58E05.

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