{"paper":{"title":"Periodic solutions for nonlinear evolution equations at resonance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Piotr Kokocki","submitted_at":"2015-05-01T11:20:31Z","abstract_excerpt":"We are concerned with periodic problems for nonlinear evolution equations at resonance of the form $\\dot u(t) = - A u(t) + F (t,u(t))$, where a densely defined linear operator $A\\colon D(A)\\to X$ on a Banach space $X$ is such that $-A$ generates a compact $C_0$ semigroup and $F\\colon [0,+\\infty)\\times X \\to X$ is a nonlinear perturbation. Imposing appropriate Landesman--Lazer type conditions on the nonlinear term $F$, we prove a formula expressing the fixed point index of the associated translation along trajectories operator, in the terms of a time averaging of $F$ restricted to $\\mathrm{Ker}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00156","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"}