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2012 | 10 | 6 | 2240-2263
Tytuł artykułu

Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study several aspects of a generalized Perron-Frobenius and Krein-Rutman theorems concerning spectral properties of a (possibly unbounded) linear operator on a cone in a Banach space. The operator is subject to the so-called tangency or weak range assumptions implying the resolvent invariance of the cone. The further assumptions rely on relations between the spectral and essential spectral bounds of the operator. In general we do not assume that the cone induces the Banach lattice structure into the underlying space.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
6
Strony
2240-2263
Opis fizyczny
Daty
wydano
2012-12-01
online
2012-10-12
Twórcy
  • Faculty of Mathematics and Computer Sciences, Nicolaus Copernicus University, Chopina 12/18, 87-100, Toruń, Poland, hannibal@mat.umk.pl
  • Faculty of Mathematics and Computer Sciences, Nicolaus Copernicus University, Chopina 12/18, 87-100, Toruń, Poland, wkrysz@mat.umk.pl
Bibliografia
  • [1] Akhmerov R.R., Kamenskii M.I., Potapov A.S., Rodkina A.E., Sadovskii B.N., Measures of Noncompactness and Condensing Operators, Oper. Theory Adv. Appl., 55, Birkhäuser, Basel, 1992
  • [2] Aliprantis C.D., Burkinshaw O., Positive Operators, Springer, Dordrecht, 2006
  • [3] Appell J., De Pascale E., Vignoli A., Nonlinear Spectral Theory, Walter De Gruyter, Berlin, 2004 http://dx.doi.org/10.1515/9783110199260[Crossref]
  • [4] Arendt W., Grabosch A., Greiner G., Groh U., Lotz H.P., Moustakas U., Nagel R., Neubrander F., Schlotterbeck U., One-Parameter Semigroups of Positive Operators, Lecture Notes in Math., 1184, Springer, Berlin, 1986
  • [5] Aubin J.-P., Ekeland I., Applied Nonlinear Analysis, Pure Appl. Math. (N.Y.), John Wiley & Sons, New York, 1984
  • [6] Barbu V., Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leiden, 1976 http://dx.doi.org/10.1007/978-94-010-1537-0[Crossref]
  • [7] Brézis H., Browder F.E., A general principle on ordered sets in nonlinear functional analysis, Advances in Math., 1976, 21(3), 355–364 http://dx.doi.org/10.1016/S0001-8708(76)80004-7[Crossref]
  • [8] Deimling K., Nonlinear Functional Analysis, Springer, Berlin, 1985 http://dx.doi.org/10.1007/978-3-662-00547-7[Crossref]
  • [9] Edmunds D.E., Potter A.J.B., Stuart C.A., Non-Compact Positive Operators, Proc. Roy. Soc. London Ser. A, 1972, 328(1572), 67–81 http://dx.doi.org/10.1098/rspa.1972.0069[Crossref]
  • [10] Engel K.-J., Nagel R., One-Parameter Semigroups for Linear Evolution Equations, Grad. Texts in Math., 194, Springer, New York, 2000
  • [11] Greiner G., Voigt J., Wolff M., On the spectral bound of the generator of semigroups of positive operators, J. Operator Theory, 1981, 5(2), 245–256
  • [12] Kamenskii M., Obukhovskii V., Zecca P., Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, de Gruyter Ser. Nonlinear Anal. Appl., 7, Walter de Gruyter, Berlin, 2001
  • [13] Kato T., Perturbation Theory for Linear Operators, Grundlehren Math. Wiss., 132, Springer, New York, 1966
  • [14] Kobayashi Y., Difference approximation of Cauchy problems for quasi-dissipative operators and generation of nonlinear semigroups, J. Math. Soc. Japan, 1975, 27(4), 640–665 http://dx.doi.org/10.2969/jmsj/02740640[Crossref]
  • [15] Krasnosel’skij M.A., Lifshits Je.A., Sobolev A.V., Positive Linear Systems, Sigma Ser. Appl. Math., 5, Heldermann, Berlin, 1989
  • [16] Mallet-Paret J., Nussbaum R.D., Generalizing the Krein-Rutman theorem, measures of noncompactness and the fixed point index, J. Fixed Point Theory Appl., 2010, 7(1), 103–143 http://dx.doi.org/10.1007/s11784-010-0010-3[Crossref][WoS]
  • [17] Martin R.H., Jr., Nonlinear Operators and Differential Equations in Banach Spaces, Pure Appl. Math. (N.Y.), John Wiley & Sons, New York-London-Sydney, 1976
  • [18] Nagel R., Uhlig H., An abstract Kato inequality for generators of positive operators semigroups on Banach lattices, J. Operator Theory, 1981, 6(1), 113–123
  • [19] van Neerven J., The asymptotic behaviour of semigroups of linear operators, Oper. Theory Adv. Appl., 88, Birkhäuser, Basel, 1996 http://dx.doi.org/10.1007/978-3-0348-9206-3[Crossref]
  • [20] Nussbaum R.D., The radius of the essential spectrum, Duke Math. J., 1970, 37, 473–478 http://dx.doi.org/10.1215/S0012-7094-70-03759-2[Crossref]
  • [21] Nussbaum R.D., Positive operators and elliptic eigenvalue problems, Math. Z., 1984, 186(2), 247–264 http://dx.doi.org/10.1007/BF01161807[Crossref]
  • [22] Nussbaum R.D., Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem, In: Fixed Point Theory, Sherbrooke, June 2–21, 1980, Lecture Notes in Math., 886, Springer, Berlin-New York, 1981, 309–330
  • [23] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci., 44, Springer, New York, 1983 http://dx.doi.org/10.1007/978-1-4612-5561-1[Crossref]
  • [24] Vrabie I.I., Compactness Methods for Nonlinear Evolutions, Pitman Monogr. Surveys Pure Appl. Math., 32, Longman Scientific & Technical, Harlow; John Wiley & Sons, New York, 1987
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0118-3
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