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Bulletin of the London Mathematical Society Advance Access originally published online on August 29, 2008
Bulletin of the London Mathematical Society 2008 40(6):972-984; doi:10.1112/blms/bdn079
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© 2008 London Mathematical Society

Spectrum in an unbounded interval for a class of nonhomogeneous differential operators

Mihai Mihailescu

Department of Mathematics
University of Craiova
200585 Craiova
Romania
and
Department of Mathematics
Central European University
1051 Budapest
Hungary
mmihailes@yahoo.com

Vicentiu Radulescu

Department of Mathematics
University of Craiova
200585 Craiova
Romania
and
Institute of Mathematics of the Romanian Academy
PO Box 1-764
014700 Bucharest
Romania

Received 6 December 2007. Revision received 20 March 2008.

The present paper deals with the spectrum of a nonhomogeneous problem involving variable exponents on an exterior domain in RN. The existence of two positive real numbers {lambda}0 and {lambda}1, is established satisfying the condition {lambda}0≤{lambda}1, such that the problem has no eigenvalue in the interval (0, {lambda}0) while any number in the interval [{lambda}1, {infty}) is an eigenvalue.

2000 Mathematics Subject Classification 35D05, 35J60, 35J70, 58E05.

The authors have been supported by Grant CNCSIS PNII–79/2007 ‘Degenerate and Singular Nonlinear Processes’. V. Radulescu has also been supported by Grants 2-CEx06-11-18/2006 and GAR-18/315/2008.


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