{"paper":{"title":"Periodic solutions to Klein-Gordon systems with linear couplings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guijuan Chang, Jianyi Chen, Jing Zhao, Zhitao Zhang","submitted_at":"2021-01-15T02:20:12Z","abstract_excerpt":"In this paper, we study the nonlinear Klein-Gordon systems arising from relativistic physics and quantum field theories\n  $$\\left\\{\\begin{array}{lll} u_{tt}- u_{xx} +bu + \\varepsilon v + f(t,x,u) =0,\\; v_{tt}- v_{xx} +bv + \\varepsilon u + g(t,x,v) =0\n  \\end{array}\\right.\n  $$ where $u,v$ satisfy the Dirichlet boundary conditions on spatial interval $[0, \\pi]$, $b>0$ and $f$, $g$ are $2\\pi$-periodic in $t$. We are concerned with the existence, regularity and asymptotic behavior of time-periodic solutions to the linearly coupled problem as $\\varepsilon$ goes to 0. Firstly, under some superlinear"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.05937","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/2101.05937/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"}