{"paper":{"title":"On coupled Schr\\\"odinger systems with double critical exponents and indefinite weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenming Zou, Xuexiu Zhong","submitted_at":"2015-03-31T05:12:12Z","abstract_excerpt":"By using variational methods, we study the existence of mountain pass solution to the following doubly critical Schr\\\"{o}dinger system: $$\n  \\begin{cases}\n  -\\Delta u-\\mu_1\\frac{u}{|x|^2}-|u|^{2^{*}-2}u &=h(x)\\alpha|u|^{\\alpha-2}|v|^\\beta u\\quad \\rm{in}\\; \\R^N,\n  -\\Delta v-\\mu_2\\frac{v}{|x|^2}-|v|^{2^{*}-2}v &= h(x)\\beta |u|^{\\alpha}|v|^{\\beta-2}v\\quad \\rm{in}\\; \\R^N,\n  \\end{cases} $$ where $\\alpha\\geq 2, \\beta\\geq 2, \\alpha+\\beta\\leq 2^*$;\\; $ \\mu_1, \\mu_2\\in [0, \\frac{(N-2)^2}{4})$. The weight function $h(x)$ is allowed to be sign-changing so that the nonlinearities include a large class of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08917","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"}