{"paper":{"title":"Continuums of positive solutions for classes of non-autonomous and non-local problems with strong singular term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlos Alberto Santos, Lais Santos, Pawan Kumar Mishra","submitted_at":"2018-11-13T00:07:25Z","abstract_excerpt":"In this paper, we show existence of \\textit{continuums} of positive solutions for non-local quasilinear problems with strongly-singular reaction term on a bounded domain in $\\mathbb{R}^N$ with $N \\geq 2$. We approached non-autonomous and non-local equations by applying the Bifurcation Theory to the corresponding $\\epsilon$-perturbed problems and using a comparison principle for $W_{\\mathrm{loc}}^{1,p}(\\Omega)$-sub and supersolutions to obtain qualitative properties of the $\\epsilon$-\\textit{continuum} limit. Moreover, this technique empowers us to study a strongly-singular and non-homogeneous "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05051","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"}