Kolmogorov equations perturbed by an inverse-square potential

Gisèle Ruiz Goldstein; Jerome A. Goldstein; Abdelaziz Rhandi

doi:10.3934/dcdss.2011.4.623

Article Contents

2011, Volume 4, Issue 3: 623-630. Doi: 10.3934/dcdss.2011.4.623

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Kolmogorov equations perturbed by an inverse-square potential

1.
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152
2.
Dipartimento di Ingegneria dell'Informazione e Matematica Applicata, Università degli Studi di Salerno, Via Ponte Don Melillo, 84084 Fisciano (Sa)

Received: March 31, 2009

Revised: October 31, 2009

Published: May 2011

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Abstract

In this paper we present a nonexistence result of exponentially bounded positive solutions to a parabolic equation of Kolmogorov type with a more general drift term perturbed by an inverse square potential. This result generalizes the one obtained in [8]. Next we introduce some classes of nonlinear operators, related to the filtration operators and the $p$-Laplacian, and involving Kolmogorov operators. We establish the maximal monotonicity of some of these operators. In the third part we discuss the possibility of some nonexistence results in the context of singular potential perturbations of these nonlinear operators.

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Mathematics Subject Classification: Primary: 35K15, 35K65, 35R05; Secondary: 35B25, 34G10, 47D08.

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References

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