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March  2011, 10(2): 701-708. doi: 10.3934/cpaa.2011.10.701

## An eigenvalue problem possessing a continuous family of eigenvalues plus an isolated eigenvalue

 1 Department of Mathematics, University of Craiova, 200585 Craiova, Romania

Received  May 2010 Revised  July 2010 Published  December 2010

In this paper we analyze an eigenvalue problem, involving a homogeneous Neumann boundary condition, in a smooth bounded domain. We show that the problem possesses, on the one hand, a continuous family of eigenvalues and, on the other hand, exactly one more eigenvalue which is isolated in the set of eigenvalues of the problem.
Citation: Mihai Mihăilescu. An eigenvalue problem possessing a continuous family of eigenvalues plus an isolated eigenvalue. Communications on Pure & Applied Analysis, 2011, 10 (2) : 701-708. doi: 10.3934/cpaa.2011.10.701
##### References:
 [1] H. Brezis, "Analyse fonctionnelle: théorie, méthodes et applications,", Masson, (1992).   Google Scholar [2] L. Gasiński and N. S. Papagiorgiu, "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems,", Chapman & Hall, (2005).   Google Scholar [3] A. Henrot, "Extremum Problems for Eigenvalues of Elliptic Operators,", Birkh\, (2006).   Google Scholar [4] M. Mihăilescu and V. Rădulescu, Continuous spectrum for a class of nonhomogeneous differential operators,, Manuscripta Mathematica, 125 (2008), 157.  doi: doi:10.1007/s00229-007-0137-8.  Google Scholar [5] M. Mihăilescu and V. Rădulescu, Sublinear eigenvalue problems associated to the Laplace operator revisited,, Israel Journal of Mathematics, ().   Google Scholar [6] L. Payne and H. Weinberger, An optimal Poincaré inequality for convex domains,, Arch. Rational Mech. Anal., 5 (1960), 286.  doi: doi:10.1007/BF00252910.  Google Scholar [7] M. Struwe, "Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems,", Springer, (1996).   Google Scholar

show all references

##### References:
 [1] H. Brezis, "Analyse fonctionnelle: théorie, méthodes et applications,", Masson, (1992).   Google Scholar [2] L. Gasiński and N. S. Papagiorgiu, "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems,", Chapman & Hall, (2005).   Google Scholar [3] A. Henrot, "Extremum Problems for Eigenvalues of Elliptic Operators,", Birkh\, (2006).   Google Scholar [4] M. Mihăilescu and V. Rădulescu, Continuous spectrum for a class of nonhomogeneous differential operators,, Manuscripta Mathematica, 125 (2008), 157.  doi: doi:10.1007/s00229-007-0137-8.  Google Scholar [5] M. Mihăilescu and V. Rădulescu, Sublinear eigenvalue problems associated to the Laplace operator revisited,, Israel Journal of Mathematics, ().   Google Scholar [6] L. Payne and H. Weinberger, An optimal Poincaré inequality for convex domains,, Arch. Rational Mech. Anal., 5 (1960), 286.  doi: doi:10.1007/BF00252910.  Google Scholar [7] M. Struwe, "Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems,", Springer, (1996).   Google Scholar
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