Heteroclinic solutions for non-autonomous boundary value problems withsingular $\Phi$-Laplacian operators

Alberto Cabada; J. Ángel Cid

doi:10.3934/proc.2009.2009.118

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2009, Volume 2009: 118-122. Doi: 10.3934/proc.2009.2009.118 open access

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Heteroclinic solutions for non-autonomous boundary value problems with singular $\Phi$-Laplacian operators

Alberto Cabada^1, and
J. Ángel Cid^2,

1.
University of Santiago de Compostela, Department of Mathematical Analysis, Santiago de Compostela, Galicia
2.
Departamento de Matemáticas, Universidad de Jaén, Campus Las Lagunillas, Jaén

Received: July 2008

Revised: February 2009

Published online: September 2009

Abstract / Introduction Related Papers Cited by

Abstract

We prove the solvability of the following boundary value problem on the real line

$\Phi(u'(t))'=f(t,u(t),u'(t))$ on $\mathbb{R}$,
$u(-\infty)=-1,$ $u(+\infty)=1,$

with a singular $\Phi$-Laplacian operator.
We assume $f$ to be a continuous function that satisfies suitable symmetry conditions. Moreover some growth conditions in a neighborhood of zero are imposed.

Keywords:

Heteroclinic connections,
singular $\Phi$-Laplacian,
boundary value problem on the real line.

Mathematics Subject Classification: Primary: 34B40; Secondary: 34B15, 34B16.

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