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

Pages: 118 - 122, Issue Special, September 2009

 Abstract        Full Text (115.3K)              

Alberto Cabada - University of Santiago de Compostela, Department of Mathematical Analysis, Santiago de Compostela, Galicia, Spain (email)
J. Ángel Cid - Departamento de Matemáticas, Universidad de Jaén, Campus Las Lagunillas, Jaén, Spain (email)

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

Received: July 2008;      Revised: February 2009;      Published: September 2009.