| Title | COMPACT LINEAR OPERATORS VIA NONLINEAR ANALYSIS |
| Publication Type | Journal Article |
| Year of Publication | 2011 |
| Authors | EDMUNDS, DE, EVANS, WD, HARRIS, DJ |
| Secondary Title | Communications in Applied Analysis |
| Volume | 15 |
| Issue | 3 |
| Start Page | 353 |
| Pagination | 362 |
| Date Published | 08/2011 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 35P30., 47A75, 47B06, 47B40 |
| Abstract | Recent work concerning the representation of compact linear operators acting between Banach spaces is discussed. The abstract results are applied to establish the existence of an infinite sequence of certain types of eigenfunctions and associated eigenvalues of the Dirichlet problem for the p−Laplacian; comparison is made with the corresponding quantities obtained by the Lusternik-Schnirelmann procedure.
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| URL | http://www.acadsol.eu/en/articles/15/3/7.pdf |
| Short Title | COMPACT LINEAR OPERATORS VIA NONLINEAR ANALYSIS |
| Refereed Designation | Refereed |
| Full Text | REFERENCES[1] Bennewitz, C., Approximation numbers = singular eigenvalues, J. Comp. and Appl. Math. 208 (2007), 102-110.
[2] Binding, P. and Drabek, P., Sturm-liouville theory for the p-Laplacian, Studia Sci. Math. Hungar. 40 (2003), 375-396. [3] Drabek, P. and Manasevich, R., On the closed solution to some nonhomogeneous eigenvalue problems with p−Laplacian, J. Diff. Integral Equations 12 (1999), 773-788. [4] Edmunds, D. E. and Evans, W. D., Spectral theory and differential operators, Oxford University Press, Oxford, 1987. [5] Edmunds, D. E., Evans, W. D. and Harris, D. J., Representations of compact linear operators in Banach spaces and nonlinear eigenvalue problems, J. London Math. Soc. 78 (2008), 65-84. [6] Edmunds, D. E., Evans, W. D. and Harris, D. J., Representations of compact linear operators in Banach spaces and nonlinear eigenvalue problems II, to appear in the proceedings of OTAMP2008, Birkhauser-Verlag. [7] Edmunds, D. E. and Lang, J., The j-eigenfunctions and s-numbers, Math. Nachr. 283, No. 3, (2010), 463-477. [8] Fabian, M., Habala, P., Hajek, P., Santalucia, V. M., Pelant, J. and Zizler, V., Functional analysis and infinite-dimensional geometry, Springer-Verlag, New York-Berlin-Heidelberg, 2001. [9] Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces I and II, New York-Berlin-Heidelberg, 1977 and 1979. |