{"paper":{"title":"The Constrained Krasnosel'skii Formula for Parabolic Differential Inclusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Jakub Siemianowski, Wojciech Kryszewski","submitted_at":"2015-04-12T00:49:59Z","abstract_excerpt":"We consider a constrained evolution inclusions of parabolic type \\eqref{inkluzja-rozn} involving an $m$-dissipative linear operator and the source term of multivalued type in a Banach space and topological properties of the solution map. We show a relation between the constrained fixed point index of the Krasnosel'skii--Poincar\\'{e} operator of translation along trajectories associated with \\eqref{inkluzja-rozn} and the appropriately defined constrained degree of $A + F\\le 0 , \\cdot \\pr $ of the right-hand side in \\eqref{inkluzja-rozn}. Our results extend those of \\cite{cw} and \\cite{gab-krysz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02924","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}