{"paper":{"title":"Quasilinear problems involving a perturbation with quadratic growth in the gradient and a noncoercive zeroth order term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Boussad Hamour, Fran\\c{c}ois Murat","submitted_at":"2015-10-15T18:21:12Z","abstract_excerpt":"In this paper we consider the problem u in H^1_0 (Omega), - div (A(x) Du) = H(x, u, Du) + f(x) + a_0 (x) u in D'(Omega), where Omega is an open bounded set of R^N, N \\geq 3, A(x) is a coercive matrix with coefficients in L^\\infty(Omega), H(x, s, xi) is a Carath\\'eodory function which satisfies for some gamma > 0 -c_0 A(x) xi xi \\leq H(x, s, xi) sign (s) \\leq gamma A(x) xi xi a.e. x in Omega, forall s in R, forall xi in R^N, f belongs to L^{N/2} (Omega), and a_0 \\geq 0 to L^q (Omega ), q > N/2. For f and a_0 sufficiently small, we prove the existence of at least one solution u of this problem w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04653","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"}