Title | A CLASS OF MAPS RELATED TO THE SEMILINEAR SPECTRUM AND APPLICATIONS |
Publication Type | Journal Article |
Year of Publication | 2011 |
Authors | FENG, WENYING |
Secondary Title | Communications in Applied Analysis |
Volume | 15 |
Start Page | 372 |
Pagination | 380 |
Date Published | 08/2011 |
Type of Work | scientific: mathematics |
ISSN | 1083–2564 |
AMS | 39B22., 47H09, 47H10 |
Abstract | In this paper, the notion of (a, q)-L-stably solvable maps, where L is a closed Fredholm operator of index zero, is introduced. Closely related to the spectrum of semilinear operators, the class of (a, q)-L-stably solvable maps generalizes both (a, q)-stably solvable and the L-stably solvable maps that were defined previously. We prove properties for the new class of operators including the continuation principle and discuss eigenvalues. We also show its applications in the study of solvability of a nonlinear system.
|
URL | http://www.acadsol.eu/en/articles/15/3/9.pdf |
Short Title | SEMILINEAR SPECTRUM AND APPLICATION |
Refereed Designation | Refereed |
Full Text | REFERENCES[1] J. Appell, E. Giorgieri and M. Vath, On a class of maps related to the Furi-Martelli-Vignoli spectrum, Annali Mat. Pura Appl. 179 (2001), 215–228.
[2] J. Appell, E. De Pascale and A. Vignoli, A comparison of different spectra for nonlinear operators, Nonlinear Anal. TMA. 40 (2000), 73–90. [3] J. Appell, E. De Pascale and A. Vignoli, Nonlinear Spectral Theory, de Gruyter Series in Nonlinear Analysis and Applications, 10, Walter de Gruyter & Co., Berlin, 2004. [4] J. Appell, E. De Pascale and A. Vignoli, A semilinear Furi-Martelli-Vignoli spectrum. Z. Anal. Anwendungen, 20(3) (2001), 1–14. [5] A. Calamai, M. Furi and A. Vignoli, A new spectrum for nonlinear operators in Banach spaces, Nonlinear Funct. Anal. & Appl, 14 (2) (2009), 317–347. [6] C. T. Cremins and G. Infante, A semilinear A-spectrum, Discrete Contin. Dyn. Syst. Series S (2008), 1(2), 235–242. [7] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, Heidelberg, New York 1985. [8] W. Feng and J. R. L. Webb, A spectral theory for semilinear operators and its applications, Progress in Nonlinear Differential Equations and Their Applications, 40 (2000), 149–163.
[9] W. Feng, A new spectral theory for nonlinear operators and its application, Abstr. Appl. Anal. 2 (1997), 163–183. [10] M. Furi, M. Martelli, A. Vignoli, Stably solvable operators in Banach spaces, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. 60 (1976), 21–26. [11] M. Furi, M. Martelli, A. Vignoli, Contributions to the spectral theory for nonlinear operators in Banach spaces, Ann. Mat. Pura Appl. 118 (1978), 229–294. [12] M. Furi, M. Martelli, A. Vignoli, On the solvability of nonlinear operator equations in normed spaces, Ann. Mat. Pura Appl. 128 (1980), 321–343. [13] R. E. Gaines and J. Mawhin, Coincidence degree theory and nonlinear differential equations, Lecture Notes in Mathematics, 568, Springer Verlag, 1977. [14] X. Li, X. Wang and G. Chen, Pinning a complex dynamical network to its equilibrium, IEEE Transactions on Circuits and Systems-I, 51(10)(2004), 2074–2087. [15] G. Zhang and W. Feng, On the number of positive solutions of a nonlinear algebraic system, Linear Algebra and its Applications, 422 (2007) 404–421. |