{"paper":{"title":"Quasi-periodic solutions for p-Laplacian equations with jumping nonlinearity and unbounded potential terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Daxiong Piao, Xiao Ma, Yiqian Wang","submitted_at":"2013-02-04T05:44:13Z","abstract_excerpt":"In this paper, we are concerned with the boundedness of all the solutions for a kind of second order differential equations with p-Laplacian term $(\\phi_p(x'))'+a\\phi_p(x^+)-b\\phi_p(x^-)+f(x)=e(t)$, where $x^+=\\max (x,0)$, $x^- =\\max(-x,0)$, $\\phi_p(s)=|s|^{p-2}s$, $p\\geq2$, $a$ and $b$ are positive constants $(a\\not=b)$, and satisfy $\\frac{1}{a^{\\frac{1}{p}}}+\\frac{1}{b^{\\frac{1}{p}}}=2\\omega^{-1} $,where $\\omega \\in \\RR^+ \\backslash \\QQ$, the perturbation $f$ is unbounded, $e(t)\\in {\\cal C}^{6}$ is is a smooth $2\\pi_p$-periodic function on $t$, where $\\pi_p=\\frac{2\\pi(p-1)^{\\frac{1}{p}}}{p\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0586","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":""},"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"}