Normalized Eigenvectors for Nonlinear Abstract and Elliptic Operators

Journal of Differential Equations

Volumn 155, Issue 2, 1999, Pages 443-475

  Kartsatos, Athanassios G ^a   Skrypnik, Igor V ^b  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

^b INSTITUTE OF APPLIED MATHEMATICS AND MECHANICS   (Ukraine)

Author keywords

Elliptic problems; Existence of eigenvalues; M accretive operator; Maximal monotone operator; Normalized eigenvectors

Indexed keywords

EID: 0033164776     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3592     Document Type: Article

References (9)

1. Agmon S., Douglis A., Nirenberg L. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. Comm. Pure Appl. Math. 12:1959;623-727.
2. Fitzpatrick P. M., Petryshyn W. V. On the nonlinear eigenvalue problem T(u)=λC(u) involving noncompact abstract and differential operators. Boll. Un. Mat. Ital. 15:1978;80-107.
3. Guan Z., Kartsatos A. G. On the eigenvalue problem for perturbations of nonlinear accretive and monotone operators in Banach spaces. Nonlinear Anal. 27:1996;125-141.
4. Kartsatos A. G. New results in the perturbation theory of maximal monotone and m-accretive operators in Banach spaces. Trans. Amer. Math. Soc. 348:1996;1663-1707.
5. Krasnosel'skij M. A. Topological Methods in the Theory of Nonlinear Integral Equations. 1964;Pergamon Press, Oxford.
6. Skrypnik I. V. The spectrum of a certain class of nonlinear operators. Dokl. Akad. Nauk Ukrain. RSR Ser. A. 12:1970;998-1000.
7. Skrypnik I. V. Nonlinear Higher Order Elliptic Equations. 1973;Naukova Dumka, Kiev.
8. Skrypnik I. V. Methods for Analysis of Nonlinear Elliptic Boundary Value Problems. Amer. Math. Soc. Transl. Ser. 2. 139:1994;Am. Math. Soc. Providence.
9. Zvyagin V. G. The existence of a continuous branch for the eigenfunctions of a nonlinear elliptic boundary value problem. Differentsial'nye Uravneniva. 13:1977;1524-1527.