{"paper":{"title":"Landesman-Lazer conditions at half-eigenvalues of the p-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bryan P. Rynne, Fran\\c{c}ois Genoud","submitted_at":"2012-07-10T20:54:22Z","abstract_excerpt":"We study the existence of solutions of the Dirichlet problem {gather} -\\phi_p(u')' -a_+ \\phi_p(u^+) + a_- \\phi_p(u^-) -\\lambda \\phi_p(u) = f(x,u), \\quad x \\in (0,1), \\label{pb.eq} \\tag{1} u(0)=u(1)=0,\\label{pb_bc.eq} \\tag{2} {gather} where $p>1$, $\\phi_p(s):=|s|^{p-1}\\sgn s$ for $s \\in \\mathbb{R}$, the coefficients $a_\\pm \\in C^0[0,1]$, $\\lambda \\in \\mathbb{R}$, and $u^\\pm := \\max\\{\\pm u,0\\}$. We suppose that $f\\in C^1([0,1]\\times\\mathbb{R})$ and that there exists $f_\\pm \\in C^0[0,1]$ such that $\\lim_{\\xi\\to\\pm\\infty} f(x,\\xi) = f_\\pm(x)$, for all $x \\in [0,1]$. With these conditions the probl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2489","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"}