{"id":"W1982204508","doi":"10.3934/dcds.2014.34.2561","title":"Liouville type results and regularity of the extremal solutions of biharmonic equation with negative exponents","year":2013,"lang":"en","type":"article","venue":"Discrete and Continuous Dynamical Systems","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":22,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Innovation Scientists and Technicians Troop Construction Projects of Henan Province; Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Biharmonic equation; Type (biology); Mathematics; Mathematical physics; Combinatorics; Boundary value problem; Boundary (topology); Mathematical analysis; Pure mathematics; Physics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001826949,0.0001118205,0.0002819179,0.00003417986,0.00009480963,0.00003174765,0.00009124607,0.00007313276,0.000005992214],"category_scores_gemma":[0.0003260612,0.00006831908,0.0000410974,0.0001567584,0.0002085494,0.00009250938,0.00008387616,0.00008993408,0.000001110005],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001559071,"about_ca_system_score_gemma":0.00002399717,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001244095,"about_ca_topic_score_gemma":0.0002452139,"domain_scores_codex":[0.9988655,0.0001781694,0.0004091086,0.0001698599,0.0002234751,0.0001539282],"domain_scores_gemma":[0.9989426,0.0002471661,0.0002978234,0.0002474809,0.0002091176,0.00005583233],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.001383143,0.001393953,0.02878508,0.001835678,0.001290722,0.000004027597,0.009593861,0.0001810451,0.1799578,0.7685115,0.0008055107,0.006257754],"study_design_scores_gemma":[0.007863148,0.001784665,0.2345307,0.002435762,0.0009366843,0.00004133695,0.006800352,0.6612678,0.004914388,0.07828896,0.0000659962,0.001070278],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9915925,0.00009655138,0.006814921,0.0001773963,0.0000731652,0.0007056867,0.00007651639,0.00001658925,0.0004466733],"genre_scores_gemma":[0.9990852,0.000006695074,0.0004876528,0.0000026608,0.00002394587,0.0000274866,0.0000151263,0.00001154287,0.000339684],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6902225,"threshold_uncertainty_score":0.2785971,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04254033058889266,"score_gpt":0.2605635067074239,"score_spread":0.2180231761185312,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}