{"id":"W1969258421","doi":"10.1016/j.jmaa.2007.01.020","title":"On a class of periodic quasilinear Schrödinger equations involving critical growth in <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"><mml:msup><mml:mi mathvariant=\"double-struck\">R</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>","year":2007,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":29,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Space (punctuation); Class (philosophy); Schrödinger equation; Nonlinear system; Mathematical physics; Conservation law; Mathematical analysis; Physics; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":false,"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":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001588299,0.0003266271,0.0004906422,0.0005444027,0.0005381544,0.0003385008,0.0005444243,0.000471531,0.001552903],"category_scores_gemma":[0.002207171,0.0003813424,0.0008420476,0.001091013,0.0004779065,0.000401691,0.0002649062,0.0007343886,0.0002052272],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000259165,"about_ca_system_score_gemma":0.0002991291,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001012812,"about_ca_topic_score_gemma":0.0002145949,"domain_scores_codex":[0.9958141,0.0001292687,0.001841422,0.0004695144,0.001145721,0.0005999851],"domain_scores_gemma":[0.9947349,0.002802613,0.001051352,0.0007231242,0.0002748946,0.0004130499],"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":[0.0001459435,0.0008502254,0.00002002507,0.0004511334,0.0007289024,0.00004964667,0.0007919288,0.0003087385,0.001958045,0.9940822,0.0003040624,0.0003091966],"study_design_scores_gemma":[0.00130761,0.0004695471,0.0001243568,0.0005799926,0.00311591,0.0002214694,0.001586048,0.9027607,0.03275286,0.0563949,0.0001718608,0.0005147276],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8122249,0.0001219869,0.1833711,0.0007653554,0.00008544323,0.00008037161,0.00009181829,0.00004320696,0.003215733],"genre_scores_gemma":[0.9702349,0.00009376602,0.02875051,0.0001398189,0.0003990637,0.0001639114,0.00008174958,0.00009295245,0.00004330387],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9376873,"threshold_uncertainty_score":0.9998639,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0309807471207586,"score_gpt":0.2946817444651905,"score_spread":0.2637009973444319,"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."}}