Topological Degree Theory and Applications (Mathematical by Yeol Je Cho,Yu-Qing Chen

because the Sixties, many researchers have prolonged topological measure idea to varied non-compact variety nonlinear mappings, and it has turn into a helpful instrument in nonlinear research. featuring a survey of advances made in generalizations of measure idea prior to now decade, this publication specializes in topological measure thought in normed areas and its functions.

The authors commence via introducing the Brouwer measure thought in Rn, then ponder the Leray-Schauder measure for compact mappings in normed areas. subsequent, they discover the measure thought for condensing mappings, together with functions to ODEs in Banach areas. this is often via a learn of measure thought for A-proper mappings and its purposes to semilinear operator equations with Fredholm mappings and periodic boundary price difficulties. the point of interest then turns to building of Mawhin's accident measure for L-compact mappings, by way of a presentation of a level thought for mappings of sophistication (S+) and its perturbations with different monotone-type mappings. the ultimate bankruptcy experiences the fastened element index thought in a cone of a Banach house and offers a striking new mounted element index for countably condensing maps.

Examples and workouts supplement every one bankruptcy. With its mix of previous and new options, Topological measure conception and functions varieties a superb textual content for self-study or certain subject matters classes and a useful reference for a person operating in differential equations, research, or topology.