{"paper":{"title":"Existence and multiplicity results for some generalized Hammerstein equations with a parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Feliz Minh\\'os, Luc\\'ia L\\'opez-Somoza","submitted_at":"2018-11-14T23:40:32Z","abstract_excerpt":"This paper considers the existence and multiplicity of fixed points for the integral operator \\begin{equation*} {\\mathcal{T}}u(t)=\\lambda \\,\\int_{0}^{T}k(t,s)\\,f(s,u(s),u^{\\prime }(s),\\dots ,u^{(m)}(s))\\,\\dif s,\\quad t\\in \\lbrack 0,T]\\equiv I, \\end{equation*} where $\\lambda >0$ is a positive parameter, $k:I\\times I\\rightarrow \\mathbb{R% }$ is a kernel function such that $k\\in W^{m,1}\\left( I\\times I\\right) $, $m$ is a positive integer with $m\\geq 1$, and $f:I\\times \\mathbb{R}^{m+1}\\rightarrow \\lbrack 0,+\\infty \\lbrack $ is a $L^{1}$-Carath\\'{e}odory function.\n  The existence of solutions for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06118","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"}