{"paper":{"title":"Spectral and topological methods in the study of solvability of semilinear equations in Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Przemys{\\l}aw Zieli\\'nski","submitted_at":"2014-05-30T10:36:04Z","abstract_excerpt":"The main goal of this dissertation is to find conditions which will guarantee the existence of solutions in the Hilbert space $H$ of semilinear equation \\[ L u+N(u)=h \\] where $L$ is a linear and self-adjoint operator, $N$ a non-linear mapping and $h\\in H$. In this project we concentrate on the case when $0$ belongs to the essential spectrum of operator $L$ which was not previously studied in this general setting.\n  In chapter 2 we additionally assume that $0$ is the infimum of the essential spectrum of $L$. We apply the degree theory for densely defined mappings of class $(S_+)$ to the operat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7817","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"}