{"paper":{"title":"On elliptic problems with mixed operators and Dirichlet-Neumann boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lovelesh Sharma, Tuhina Mukherjee","submitted_at":"2023-11-05T04:57:56Z","abstract_excerpt":"In this paper, we study the existence, nonexistence and multiplicity of positive solutions to the problem given by\n  \\begin{equation*} \\label{1}\n  \\left\\{\\begin{split} \\mathcal{L}u\\: &= \\lambda u^{q} + u^{p}, \\quad u>0 ~~ \\text{in} ~\\Omega,\n  u&=0~~\\text{in} ~~{D^c},\n  \\mathcal{N}_s(u)&=0 ~~\\text{in} ~~{\\Pi_2},\n  \\frac{\\partial u}{\\partial \\nu}&=0 ~~\\text{in}~~ \\partial \\Omega \\cap \\overline{\\Pi_2}.\n  \\end{split} \\right.\\tag{$P_\\lambda$} \\end{equation*}\n  {where $D= \\left(\\Omega \\cup {\\Pi_2} \\cup (\\partial\\Omega\\cap\\overline{\\Pi_2})\\right)$ and $D^c$ is the complement of $D$, $\\Omega \\subseteq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.02567","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.02567/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}