{"paper":{"title":"A class of semilinear elliptic equations on lattice graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"B. Hua, L. Wang, R. Li","submitted_at":"2022-03-10T04:04:55Z","abstract_excerpt":"In this paper, we study the semilinear elliptic equation of the form \\begin{eqnarray*} -\\Delta u+a(x)|u|^{p-2}u-b(x)|u|^{q-2}u=0 \\end{eqnarray*} on lattice graphs $\\mathbb{Z}^{N}$, where $N\\geq 2$ and $2\\leq p<q<+\\infty$. By the Br\\'{e}zis-Lieb lemma and concentration compactness principle, we prove the existence of positive solutions to the above equation with constant coefficients $\\bar{a},\\bar{b}$ and the decomposition of bounded Palais-Smale sequences for the functional with variable coefficients, which tend to some constants $\\bar{a},\\bar{b}$ at infinity, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.05146","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.05146/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"}