A topological introduction to nonlinear analysis /
[Book]
Robert F. Brown.
2nd ed.
Boston :
Birkhäuser,
c2004.
xi, 184 p. :
ill. ;
24 cm.
Includes bibliographical references (p. [181]) and index.
Fixed point existence theory. The topological point of view ; Ascoli-arzela theory ; Brouwer fixed point theory ; Schauder fixed point theory ; The forced pendulum ; Equilibrium heat distribution ; Generalized Bernstein theory -- Degree theory. Brouwer degree ; Properties of the Brouwer Degree ; Leray-Schauder degree ; Properties of the Leray-Schauder Degree ; The Mawhin operator ; The pendulum swings back -- Bifurcation theory. A separation theorem ; Compact linear operators ; The degree calculation ; The Krasnoselskii-Rabinowitz bifurcation theorem ; Nonlinear Sturm-Liouville theory ; More Sturm-Liouville theory ; Euler buckling -- Appendices. Singular homology ; Additivity and product properties ; Bounded linear transformations.