{"id":1876,"date":"2026-03-16T14:15:57","date_gmt":"2026-03-16T13:15:57","guid":{"rendered":"https:\/\/umi.dm.unibo.it\/jm-ita-bra-2026\/?page_id=1876"},"modified":"2026-03-16T14:15:57","modified_gmt":"2026-03-16T13:15:57","slug":"special-session-12","status":"publish","type":"page","link":"https:\/\/umi.dm.unibo.it\/jm-ita-bra-2026\/special-sessions\/special-session-12\/","title":{"rendered":"Special Session 12 – Topological methods for the qualitative analysis of differential equations"},"content":{"rendered":"

Special Session 12<\/h1>\n

Topological methods for the qualitative analysis of differential equations<\/h2>\n

Organizers: <\/strong>Pierluigi Benevieri (University of S\u00e3o Paulo, Brazil), Alessandro Calamai (Marche Polytechnic University, Italy), Gennaro Infante (University of Calabria, Italy)<\/p>\n

MSC codes:<\/strong> 35C-XX<\/p>\n

Description:<\/strong> By the expression \u201ctopological methods\u201d we usually denote the family of tools such as, among others, the topological degree, the fixed point index, the shooting method, the lower and upper solutions method. Those have been proved, for many decades, to be fundamental instruments in the investigation of qualitative properties of solutions to differential equations, particularly (but not only) when the problems do not have a variational structure. Topological methods are particularly useful for addressing problems such as the existence, multiplicity, localization of solutions, as well as for studying the local and global bifurcation of solutions or their stability in relation to perturbations of the problem. We mention for example the use of the contraction theorem to prove the local existence and uniqueness of solutions to the classical Cauchy problem, and the application of topological degree to elliptic equations, as in the pioneering work of J. Leray and J. Schauder in 1934, in which the two authors defined the degree that would be named after them. The current research now focuses on the application of topological methods to the study of the most varied classes of differential systems: partial differential equations, ordinary differential equations, delay equations, functional differential equations, differential inclusions, time-scale equations, measure equations, and impulsive equations. A common feature of the topological techniques used in nonlinear analysis and in the theory of dynamical systems is that they provide information about the problem under consideration thanks to the topological structure of the spaces in which the problem can be studied and the topological properties of the operators involved, both linear and nonlinear. When studying a system of differential equations, the idea behind the application of a topological method is to transform the initial problem into a functional equation (or system) involving nonlinear operators between spaces of functions, which usually are normed, Banach or Hilbert spaces. This section aims to bring together highly qualified colleagues in the field, giving them the opportunity to present their recent results, in order to foster the exchange and dissemination of ideas among the section’s participants and, more generally, the meeting conference.<\/p>\n<\/div><\/section>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":6,"featured_media":0,"parent":210,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1876","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/umi.dm.unibo.it\/jm-ita-bra-2026\/wp-json\/wp\/v2\/pages\/1876","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/umi.dm.unibo.it\/jm-ita-bra-2026\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/umi.dm.unibo.it\/jm-ita-bra-2026\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/umi.dm.unibo.it\/jm-ita-bra-2026\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/umi.dm.unibo.it\/jm-ita-bra-2026\/wp-json\/wp\/v2\/comments?post=1876"}],"version-history":[{"count":2,"href":"https:\/\/umi.dm.unibo.it\/jm-ita-bra-2026\/wp-json\/wp\/v2\/pages\/1876\/revisions"}],"predecessor-version":[{"id":1878,"href":"https:\/\/umi.dm.unibo.it\/jm-ita-bra-2026\/wp-json\/wp\/v2\/pages\/1876\/revisions\/1878"}],"up":[{"embeddable":true,"href":"https:\/\/umi.dm.unibo.it\/jm-ita-bra-2026\/wp-json\/wp\/v2\/pages\/210"}],"wp:attachment":[{"href":"https:\/\/umi.dm.unibo.it\/jm-ita-bra-2026\/wp-json\/wp\/v2\/media?parent=1876"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}