{"id":"W2073348811","doi":"10.1007/s00526-013-0694-5","title":"Infinitely many positive solutions for nonlinear equations with non-symmetric potentials","year":2013,"lang":"en","type":"article","venue":"Calculus of Variations and Partial Differential Equations","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":44,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Degeneracy (biology); Combinatorics; Nonlinear system; Energy (signal processing); Mathematical physics; 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"],"consensus_categories":[],"category_scores_codex":[0.0003420712,0.0004375286,0.0006718272,0.000622155,0.001098436,0.0002490898,0.000282292,0.0002459289,0.0006201073],"category_scores_gemma":[0.002110182,0.0003925796,0.000300195,0.00100647,0.0002935494,0.0005637327,0.0001602477,0.0002429111,0.00005449452],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006846921,"about_ca_system_score_gemma":0.0002740201,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005205533,"about_ca_topic_score_gemma":0.0002186224,"domain_scores_codex":[0.9967741,0.000192434,0.001188264,0.0005654124,0.0005299129,0.0007499005],"domain_scores_gemma":[0.9942466,0.002786211,0.0006078613,0.0005813602,0.001439277,0.0003387023],"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":[0.0000493274,0.0009660115,0.00002293603,0.00008385691,0.0003912181,4.920748e-7,0.0005481869,0.0003703569,0.007328092,0.9875807,0.0003063211,0.00235246],"study_design_scores_gemma":[0.002516296,0.0005782055,0.003001357,0.000130613,0.001184139,0.000004103119,0.0002105011,0.9690695,0.002605668,0.01993281,0.0001424474,0.0006243362],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02121082,0.00004285419,0.97312,0.001013768,0.0002942192,0.002540911,0.00123981,0.0001156136,0.0004220253],"genre_scores_gemma":[0.9757687,0.00001543221,0.02118396,0.00005276813,0.0003868428,0.001147142,0.0009381538,0.00007824643,0.0004287616],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9686992,"threshold_uncertainty_score":0.9998526,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05472253905336382,"score_gpt":0.3026429804200113,"score_spread":0.2479204413666475,"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."}}