Fixed points and topological degree in nonlinear analysis

摘要: The topological methods based on fixed-point theory and local degree which have been developed by Leray, Schauder, Nirenberg, Cesari others for the study of nonlinear differential equations are here described in detail, beginning with elementary considerations. reader is not assumed to any knowledge topology beyond point sets Euclidean n-space ordinarily forms part a course advanced calculus. first applied existence stability periodic almost-periodic solutions systems ordinary equations, both quasi-linear 'large' nonlinearities. Then, after being extended infinite-dimensional 'function-spaces', these integral partial further problems concerning equations.