{"paper":{"title":"Fractional Hamiltonian systems with critical exponential growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacques Giacomoni, Joao Marcos do \\'O, Pawan Kumar Mishra","submitted_at":"2018-11-11T08:20:05Z","abstract_excerpt":"In this paper, we study the following nonlocal nonautonomous Hamiltonian system on whole $\\mathbb R$ $$ \\left\\{\\begin{array}{ll} (-\\Delta)^\\frac12~ u +u=Q(x) g(v)&\\quad\\mbox{in } \\mathbb R,\\\\ (-\\Delta)^\\frac12~ v+v = P(x)f(u)&\\quad\\mbox{in } \\mathbb R, \\end{array}\\right. $$ where $(-\\Delta)^\\frac12$ is {the} square root Laplacian operator. We assume that the nonlinearities $f, g$ have critical growth at $+\\infty$ in the sense of Trudinger-Moser inequality and the nonnegative weights $P(x)$ and $Q(x)$ vanish at $+\\infty$. Using suitable variational method combined with {the} generalized linking"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04368","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"}