References
- X. Bai, Y. W. Wang, et al. (2009). Definition and criterion of homogeneous generalized inverse. Acta Math. Sinica Chin. Ser. A 52:353–360.
- V. Barbu and T. Precupanu (1978). Convexity and Optimization in Banach Spaces. Sijthoff and Noordhoff, Leyden.
- M. G. Crandall and P. H. Rabinnowitz (1971). Bifurcation from simple eigenvalues. J. Func. Anal. 8:321–340.
- M. G. Crandall and P. H. Rabinowitz (1972). Bifurcation, perturbation of simple eigenvalues and linearized stabilit. Arch. Rational Mech. Anal. 52:161–181.
- F. Deutsch (1982). Linear selections for the metric projection. J. Funct. Anal. 49:269–292.
- J. Diestel (1975). Geometry of Banach Spaces-selected Topics, Lecture Notes in Mathematics. Springer-Verlag, New York/Berlin.
- H. W. Engl and M. Z. Nashed (1981). New extremal characterization of generalized inverses of linear operators. J. Math. Anal. Appl. 82:566–586.
- R. B. Holmes (1975). Geometric Functional Analysis and its Applications. Springer-Verlager, New York/Heideberg/Berlin.
- Q. L. Huang (2011). On perturbations for oblique projection generalized inverses of closed linear operators in Banach spaces. Linear Algebra Appl. 434:2468–2474.
- H. Hudzik, Y. W. Wang, and W. J. Zheng (2008). Criteria for the metric generalized inverse and its selections in Banach spaces. Set-Valued Anal. 16:51–65.
- S. Krömer, T. J. Healey, and H. Kielhöfer (2006). Bifurcation with a two-dimensional kernel. J. Differ. Equations 220:234–258.
- J. Lindenstrauss and L. Tzafriri (1971). On the complemented subspaces problem. Israel. Math. 9:263–269.
- P. Liu, J. P. Shi, and Y. W. Wang (2007). Imperfect transcritical and Pitchfork bifurcations. J. Funct. Anal. 251:573–600.
- P. Liu and Y. W. Wang (2007). The best generalized inverse of the linear operator in normed linear space. Linear Algebra Appl. 420:9–19.
- J. P. Ma (2008). A generalized transversality in global analysis. Pacific J. Math. 236:357–371.
- M. Z. Nashed ed. (1976). Generalized Inverse and Applications. Academic Press, New York/ London.
- M. Z. Nashed (1971). Generalized inverses, normal solvability, and iteration for singular operator equations. In: Nonlinear Function analysis and Applications (L. B. Rall, ed.). Academic Press, New York, pp. 311–359.
- M. Z. Nashed (1987). Inner, outer and generalized inverses in Banach and Hilbert spaces. Numer. Funct. Anal. Optim. 9:261–325.
- M. Z. Nashed and G. F. Votruba (1974). A unified approach to generalized inverses of linear operators: I. Algebraic, topological and projectional properties. Bull. Amer. Math. Soc. 80:825–830.
- M. Z. Nashed and G. F. Votruba (1974). A unified approach to generalized inverses of linear operators: II. Extremal and proximinal properties. Bull. Amer. Math. Soc. 80:831–835.
- M. Z. Nashed and G. F. Votruba (1976). A unified operator theory of generalized inverses. In: Generalized Inverses and Applications (M. Z. Nashed, ed.). Academic Press, New York, pp. 1–109.
- J. P. Shi (2009). Bifurcation in infinite dimensional spaces and applications in spatiotemporal biological and chemical models. Front. Math. China 4:407–424.
- Y. W. Wang (2005). Generalized Inverse of Operator in Banach Spaces and Applications. Science Press, Beijing.
- Y. W. Wang and S. R. Pan (2003). An approximation problem of the finite rank operator in Banach spaces. Sci. Chin. A 46:245–250.
- H. Wang and Y. W. Wang (2003). Metric generalized inverse of linear operator in Banach space. Chin. Ann. Math. 24:509–520.
- Y. M. Wei and J. Ding (2001). Representations for Moore–Penrose inverses in Hilbert spaces. Appl. Math. Lett. 14:599–604.
- X. D. Yang and Y. W. Wang (2010). Some new perturbation theorems for generalized inverses of linear operators in Banach spaces. Linear Algebra Appl. 433:1939–1949.
- K. Yosida (1978). Functional Analysis. Springer-Verlag, New York.
- E. Zeidler (1988). Nonlinear Functional Analysis and its Applications IV. Springer-Verlag, New York/Berlin.