{"id":"W4389705449","doi":"10.23952/jnva.8.2024.1.02","title":"Multiple solutions for a class of Kirchhoff type equations with zero mass and Hardy-Littlewood-Sobolev critical nonlinearity","year":2023,"lang":"en","type":"article","venue":"Journal of Nonlinear and Variational Analysis","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"National Natural Science Foundation of China","keywords":"Sobolev space; Mathematics; Zero (linguistics); Nonlinear system; Class (philosophy); Mathematical analysis; Type (biology); Pure mathematics; Physics; Quantum mechanics; Computer science","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009278419,0.0001493529,0.000519674,0.0005578852,0.0002471557,0.0000558995,0.0001095404,0.0001007099,0.00004554885],"category_scores_gemma":[0.004240169,0.0001202073,0.0002384613,0.001166902,0.0001336088,0.0001935768,0.00005056764,0.000183124,0.000002881989],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002838429,"about_ca_system_score_gemma":0.0002244919,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002514072,"about_ca_topic_score_gemma":0.0001132708,"domain_scores_codex":[0.998271,0.0001077452,0.0007403521,0.0001848911,0.0004566309,0.0002393722],"domain_scores_gemma":[0.9945095,0.003428045,0.000386421,0.0001584088,0.001362288,0.0001553585],"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":[0.001757232,0.003284677,0.05068786,0.0008941809,0.01516755,0.00002588717,0.001976936,0.03017977,0.01828756,0.8739871,0.001667174,0.002084011],"study_design_scores_gemma":[0.001241933,0.0003541379,0.01840587,0.00004772215,0.003703873,0.00001012745,0.0001321564,0.9172524,0.0001350301,0.05819812,0.0003378847,0.0001808094],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1038321,0.00005831231,0.8926175,0.002451354,0.00009937948,0.0001831663,0.0007057068,0.00002244725,0.00003010435],"genre_scores_gemma":[0.7960243,0.00004283619,0.2032758,0.00003216668,0.0002921355,0.000008524423,0.0001808226,0.00002021543,0.0001231518],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8870726,"threshold_uncertainty_score":0.5076185,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09661493193066616,"score_gpt":0.3608712323542904,"score_spread":0.2642563004236242,"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."}}