{"paper":{"title":"Boundedness for Second Order Differential Equations with Jumping p-Laplacian and an Oscillating Term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Daxiong Piao, Xiao Ma, Yiqian Wang","submitted_at":"2013-01-23T02:52:54Z","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 and an oscillating term $(\\phi_p(x'))'+a\\phi_p(x^+)-b\\phi_p(x^-)=G_x(x,t)+f(t)$, where$x^+=\\max (x,0)$,$x^- =\\max(-x,0)$,$\\phi_p(s)=|s|^{p-2}s$,$p\\geq2$, $a $ and $b$ are positive constants $(a\\not=b)$, the perturbation $f(t)\\in {\\cal C}^{23}(\\RR/2\\pi_p \\ZZ)$, the oscillating term $G\\in {\\cal C}^{21}(\\RR\\times\\RR/2\\pi_p \\ZZ)$,where $\\pi_p=\\frac{2\\pi(p-1)^{\\frac{1}{p}}}{p\\sin\\frac{\\pi}{p}},$ and $G(x,t)$ satisfies $\\label{G} |D_x^iD_t^jG(x,t)|\\le C,\\quad 0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5388","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":""},"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"}