{"paper":{"title":"On Kirchhoff-type p(.)-Laplacian problems with sandwich-type and arbitrary growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Kirchhoff-type p(·)-Laplacian problems with arbitrary and sandwich growth admit positive bounded weak solutions.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ky Ho","submitted_at":"2026-04-10T22:06:33Z","abstract_excerpt":"We establish the existence of a positive bounded weak solution for a class of Kirchhoff-type $p(\\cdot)$-Laplacian problems involving an arbitrary growth and a sandwich-type growth $s(\\cdot)\\in (\\inf p,\\sup p)$. This setting leads to substantial analytical difficulties in the variational analysis of the associated energy functional. By combining truncation arguments with a priori estimates, we prove the existence result under suitable assumptions on the data."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish the existence of a positive bounded weak solution for a class of Kirchhoff-type p(·)-Laplacian problems involving an arbitrary growth and a sandwich-type growth s(·)∈(inf p, sup p).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Suitable assumptions on the data (growth conditions, Kirchhoff function, and variable exponents) that are not specified in the abstract but are required for the truncation and a priori estimate arguments to close.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Existence of positive bounded weak solutions is shown for Kirchhoff-type variable-exponent Laplacian problems with arbitrary and sandwich-type growth conditions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Kirchhoff-type p(·)-Laplacian problems with arbitrary and sandwich growth admit positive bounded weak solutions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b26909fe4545b1e46497febeb741a63190480208654c43b1149179a0de7cfea4"},"source":{"id":"2604.09929","kind":"arxiv","version":2},"verdict":{"id":"24ab9253-a502-4bf1-8a41-a10e9c073a25","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T16:44:29.284346Z","strongest_claim":"We establish the existence of a positive bounded weak solution for a class of Kirchhoff-type p(·)-Laplacian problems involving an arbitrary growth and a sandwich-type growth s(·)∈(inf p, sup p).","one_line_summary":"Existence of positive bounded weak solutions is shown for Kirchhoff-type variable-exponent Laplacian problems with arbitrary and sandwich-type growth conditions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Suitable assumptions on the data (growth conditions, Kirchhoff function, and variable exponents) that are not specified in the abstract but are required for the truncation and a priori estimate arguments to close.","pith_extraction_headline":"Kirchhoff-type p(·)-Laplacian problems with arbitrary and sandwich growth admit positive bounded weak solutions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.09929/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"}