{"paper":{"title":"Ground state and multiple solutions for modified autonomous fourth-order elliptic equations with Berestycki-Lions type conditions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fan Wang, Lifeng Yin","submitted_at":"2025-08-22T00:06:07Z","abstract_excerpt":"This article establishes the existence of a ground state and infinitely many solutions for the modified fourth-order elliptic equation:\n  \\[\n  \\begin{aligned}\n  \\left\\{\n  \\begin{array}{ll}\n  \\Delta^2 u - \\Delta u + u - \\frac{1}{2}u\\Delta(u^2) = f(u), & \\text{in } \\mathbb{R}^N,\n  u \\in H^2(\\mathbb{R}^N),\n  \\end{array}\n  \\right.\n  \\end{aligned}\n  \\]\n  where $4 < N \\leq 6$ and$f:\\mathbb{R}\\rightarrow\\mathbb{R}$ is a nonlinearity of Berestycki-Lions type.\n  For the ground state solution, we develop a novel approach that combines Jeanjean's technique with a Pohozaev-Palais-Smale sequence constructi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.16010","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/2508.16010/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"}