{"id":"https://openalex.org/W7130643239","doi":"https://doi.org/10.1002/mma.70611","title":"Sharp Bounds of Eigenvalue Ratios for Sturm\u2013Liouville Equations With Dirichlet Boundary Conditions","display_name":"Sharp Bounds of Eigenvalue Ratios for Sturm\u2013Liouville Equations With Dirichlet Boundary Conditions","publication_year":2026,"publication_date":"2026-02-20","ids":{"openalex":"https://openalex.org/W7130643239","doi":"https://doi.org/10.1002/mma.70611"},"language":"en","primary_location":{"id":"doi:10.1002/mma.70611","doi":"https://doi.org/10.1002/mma.70611","is_oa":false,"landing_page_url":"https://doi.org/10.1002/mma.70611","pdf_url":null,"source":{"id":"https://openalex.org/S89452420","display_name":"Mathematical Methods in the Applied Sciences","issn_l":"0170-4214","issn":["0170-4214","1099-1476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods in the Applied Sciences","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126460974","display_name":"Yu Gan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu Gan","raw_affiliation_strings":["School of Mathematical Sciences Qufu Normal University  Qufu Shandong China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences Qufu Normal University  Qufu Shandong China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056300367","display_name":"Zhaowen Zheng","orcid":"https://orcid.org/0000-0003-1976-2243","observed_orcids":["https://orcid.org/0000-0003-1976-2243"]},"institutions":[{"id":"https://openalex.org/I4210122543","display_name":"Guangdong Polytechnic Normal University","ror":"https://ror.org/02pcb5m77","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210122543"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaowen Zheng","raw_affiliation_strings":["College of Mathematics and Systems Science Guangdong Polytechnic Normal University  Guangzhou Guangdong China"],"raw_orcid":"https://orcid.org/0000-0003-1976-2243","affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science Guangdong Polytechnic Normal University  Guangzhou Guangdong China","institution_ids":["https://openalex.org/I4210122543"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100377582","display_name":"Kun Li","orcid":"https://orcid.org/0000-0003-3076-2586","observed_orcids":["https://orcid.org/0000-0003-3076-2586","https://orcid.org/0000-0002-2632-739X"]},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kun Li","raw_affiliation_strings":["School of Mathematical Sciences Qufu Normal University  Qufu Shandong China"],"raw_orcid":"https://orcid.org/0000-0002-2632-739X","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences Qufu Normal University  Qufu Shandong China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102080730","display_name":"Jing Shao","orcid":"https://orcid.org/0000-0003-0155-3742","observed_orcids":["https://orcid.org/0000-0003-0155-3742"]},"institutions":[{"id":"https://openalex.org/I42852656","display_name":"Shenyang University","ror":"https://ror.org/04ddfwm68","country_code":"CN","type":"education","lineage":["https://openalex.org/I42852656"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Shao","raw_affiliation_strings":["School of Sciences Shenyang University  Shenyang Liaoning China"],"raw_orcid":"https://orcid.org/0000-0003-0155-3742","affiliations":[{"raw_affiliation_string":"School of Sciences Shenyang University  Shenyang Liaoning China","institution_ids":["https://openalex.org/I42852656"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"USD","value_usd":5000},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"49","issue":"10","first_page":"10552","last_page":"10565"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sturm-liouville-equation","display_name":"Sturm-Liouville equation","score":0.8389999866485596},{"id":"https://openalex.org/keywords/eigenvalue-ratio","display_name":"eigenvalue ratio","score":0.8659999966621399},{"id":"https://openalex.org/keywords/dirichlet-boundary-conditions","display_name":"Dirichlet boundary conditions","score":0.972000002861023},{"id":"https://openalex.org/keywords/sharp-bounds","display_name":"sharp bounds","score":0.6919999718666077},{"id":"https://openalex.org/keywords/measure-differential-equations","display_name":"measure differential equations","score":0.6179999709129333},{"id":"https://openalex.org/keywords/nonnegative-potential","display_name":"nonnegative potential","score":0.593999981880188},{"id":"https://openalex.org/keywords/weight-functions","display_name":"weight functions","score":0.6909999847412109}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9261999726295471},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7019000053405762},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.6777999997138977},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5806999802589417},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5764999985694885},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.5674999952316284},{"id":"https://openalex.org/C102231394","wikidata":"https://www.wikidata.org/wiki/Q5280763","display_name":"Dirichlet eigenvalue","level":5,"score":0.5587000250816345},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5425000190734863},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.527899980545044},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4223000109195709},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.41499999165534973},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.40059998631477356},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3840000033378601},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.36410000920295715},{"id":"https://openalex.org/C148158259","wikidata":"https://www.wikidata.org/wiki/Q975727","display_name":"Dirichlet's principle","level":4,"score":0.3612000048160553},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3587000072002411},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3215999901294708},{"id":"https://openalex.org/C103302479","wikidata":"https://www.wikidata.org/wiki/Q1227685","display_name":"Dirichlet conditions","level":5,"score":0.28610000014305115},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.2732999920845032},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.27160000801086426},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.25609999895095825}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/mma.70611","doi":"https://doi.org/10.1002/mma.70611","is_oa":false,"landing_page_url":"https://doi.org/10.1002/mma.70611","pdf_url":null,"source":{"id":"https://openalex.org/S89452420","display_name":"Mathematical Methods in the Applied Sciences","issn_l":"0170-4214","issn":["0170-4214","1099-1476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods in the Applied Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1075438754","display_name":null,"funder_award_id":"ZR2024MA020","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G2918780324","display_name":null,"funder_award_id":"12301199","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G359293408","display_name":null,"funder_award_id":"12401160","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5824185437","display_name":null,"funder_award_id":"ZR2023MA023","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1494263571","https://openalex.org/W1559113676","https://openalex.org/W1575164542","https://openalex.org/W1608492828","https://openalex.org/W1887903210","https://openalex.org/W1973861336","https://openalex.org/W2000523938","https://openalex.org/W2026031976","https://openalex.org/W2037703523","https://openalex.org/W2044718862","https://openalex.org/W2050507412","https://openalex.org/W2051186530","https://openalex.org/W2085258825","https://openalex.org/W2090945912","https://openalex.org/W2112656850","https://openalex.org/W2137757043","https://openalex.org/W2539035108","https://openalex.org/W2796698393","https://openalex.org/W2808942422","https://openalex.org/W3097008771","https://openalex.org/W3136479896","https://openalex.org/W4232969934","https://openalex.org/W4297791536","https://openalex.org/W4311097809","https://openalex.org/W4312201175","https://openalex.org/W4386061952","https://openalex.org/W4414121195","https://openalex.org/W4414606843","https://openalex.org/W7118980862"],"related_works":["https://openalex.org/W7160890673","https://openalex.org/W4415676294","https://openalex.org/W7138897489","https://openalex.org/W4312201175","https://openalex.org/W2051186530","https://openalex.org/W2090945912","https://openalex.org/W7051438909","https://openalex.org/W2063397932","https://openalex.org/W7096699040","https://openalex.org/W4404366662"],"abstract_inverted_index":{"ABSTRACT":[0],"The":[1],"aim":[2],"of":[3,11,47,51],"this":[4],"article":[5],"is":[6,24,76],"to":[7],"prove":[8],"the":[9,15,31,44,48,56,68,74],"maximization":[10,71],"eigenvalue":[12,54],"ratios":[13],"for":[14,37,55],"general":[16],"Sturm\u2013Liouville":[17],"problem:":[18],"with":[19],"Dirichlet":[20,53],"boundary":[21],"conditions,":[22],"where":[23,60],"a":[25],"nonnegative":[26],"continuous":[27],"potential":[28],"on":[29],"and":[30,36,40,61,73],"weight":[32],"function":[33],"satisfies":[34],"that":[35],"some":[38],"constants":[39],".":[41],"By":[42],"finding":[43],"explicit":[45],"solution":[46,75],"minimization":[49],"problem":[50,72],"any":[52],"measure":[57],"differential":[58],"equation":[59],"are":[62],"two":[63],"suitable":[64],"measures,":[65],"we":[66],"solve":[67],"infinitely":[69],"dimensional":[70],"given":[77],"by":[78],"an":[79],"elementary":[80],"function.":[81]},"counts_by_year":[],"updated_date":"2026-09-27T08:07:27.782135","created_date":"2026-02-20T00:00:00"}