Abstract
Recall that L(X) is the normed linear space of bounded linear operators \(T: X \rightarrow X\).
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References
Bernstein, S.: Sur les èquations du calcul des variations. Ann. Sci. École Norm. Sup. 29, 431–485 (1912)
Brown, A., Page, A.: Elements of Functional Analysis. Van Nostrand, NewYork (1970)
Coddington, E., Levenson, N.: Theory of Ordinary Differential Equations. McGraw-Hill, NewYork (1955)
Deimling, K.: Nonlinear Functional Analysis. Springer, NewYork (1985)
Gaines, R., Mawhin, J.: Coincidence Degree and Nonlinear Differential Equations. Springer Lecture Notes in Mathematics, vol. 568, Springer, NewYork (1977)
Granas, A., Guenther, R., Lee, J.: On a theorem of S. Bernstein. Pacific J. Math. 74, 67–82 (1978)
Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)
Leggett, R., Williams, L.: Multiple positive fixed points of nonlinear operators on ordered Banach spaces. Indiana U. Math J. 28, 673–688 (1979)
Mawhin, J.: Periodic oscillations of forced pendulum-like equations. Springer Lecture Notes in Math. 964, 458–476 (1982)
Mawhin, J.: The forced pendulum: A paradigm for nonlinear analysis and dynamical systems. Expo. Math. 6, 271–287 (1988)
Nussbaum, R.: The fixed point index and some applications, Séminaire de Mathématiques Supérieures, Université de Montréal (1985)
Rabinowitz, P.: Some global results for nonlinear eigenvalue problems. J. Funct. Anal. 7, 487–513 (1971)
Ritger, P., Rose, N.: Differential Equations with Applications. McGraw-Hill, NewYork (1968)
Spanier, E.: Algebraic Topology. McGraw-Hill, NewYork (1966)
Williams, L., Leggett, R.: Unique and multiple solutions of a family of differential equations modeling chemical reactions. SIAM J. Math. Anal. 13, 122–133 (1982)
Zeidler, E.: Functional Analysis and Its Applications I: Fixed Point Theorems. Springer, NewYork (1986)
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Brown, R.F. (2014). Compact Linear Operators. In: A Topological Introduction to Nonlinear Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-11794-2_20
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DOI: https://doi.org/10.1007/978-3-319-11794-2_20
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