Infinitely many solutions to superquadratic planar Dirac-type systems

Alberto Boscaggin; Anna Capietto

doi:10.3934/proc.2009.2009.72

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2009, Volume 2009: 72-81. Doi: 10.3934/proc.2009.2009.72 open access

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Infinitely many solutions to superquadratic planar Dirac-type systems

Alberto Boscaggin^1, and
Anna Capietto^2,

1.
SISSA-ISAS International School for Advanced Studies, Via Beirut, 2-4 - 34014 Trieste
2.
Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino

Received: July 2008

Revised: April 2009

Published: August 2009

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Abstract

It is proved the existence of infinitely many solutions to a superquadratic Dirac-type boundary value problem of the form $\tau z = \nabla_z F(t,z)$, $y(0) = y(\pi) = 0$ ($z=(x,y)\in \mathbb{R}^2 $). Solutions are distinguished by using the concept of rotation number. The proof is performed by a global bifurcation technique.

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Mathematics Subject Classification: Primary: 34B15, 34C23; Secondary: 37E45.

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