{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:12:08Z","timestamp":1772291528178,"version":"3.50.1"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,9,27]],"date-time":"2019-09-27T00:00:00Z","timestamp":1569542400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,9,27]],"date-time":"2019-09-27T00:00:00Z","timestamp":1569542400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771253"],"award-info":[{"award-number":["11771253"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11701327"],"award-info":[{"award-number":["11701327"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s10957-019-01584-x","type":"journal-article","created":{"date-parts":[[2019,9,27]],"date-time":"2019-09-27T11:02:46Z","timestamp":1569582166000},"page":"842-857","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Sturm\u2013Liouville Problems Involving Distribution Weights and an Application to Optimal Problems"],"prefix":"10.1007","volume":"184","author":[{"given":"Hongjie","family":"Guo","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0716-8351","authenticated-orcid":false,"given":"Jiangang","family":"Qi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,9,27]]},"reference":[{"key":"1584_CR1","doi-asserted-by":"publisher","first-page":"4188","DOI":"10.1016\/j.jde.2009.03.016","volume":"246","author":"M Zhang","year":"2009","unstructured":"Zhang, M.: Extremal values of smallest eigenvalues of Hill\u2019s operators with potentials in L1 balls. J. Differ. Equ. 246, 4188\u20134220 (2009)","journal-title":"J. Differ. Equ."},{"key":"1584_CR2","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1016\/j.jde.2009.04.008","volume":"247","author":"Q Wei","year":"2009","unstructured":"Wei, Q., Meng, G., Zhang, M.: Extremal values of eigenvalues of Sturm\u2013Liouville operators with potentials in L1 balls. J. Differ. Equ. 247, 364\u2013400 (2009)","journal-title":"J. Differ. Equ."},{"key":"1584_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.14232\/ejqtde.2013.1.48","volume":"48","author":"D Hinton","year":"2013","unstructured":"Hinton, D.: Bounds and optimization of the minimum eigenvalue for a vibrating system. Electron. J. Qual. Theory Differ. Equ. 48, 1\u201322 (2013)","journal-title":"Electron. J. Qual. Theory Differ. Equ."},{"key":"1584_CR4","doi-asserted-by":"publisher","first-page":"035007","DOI":"10.1088\/0266-5611\/32\/3\/035007","volume":"32","author":"J Qi","year":"2016","unstructured":"Qi, J., Chen, S.: Extremal norms of the potentials recovered from inverse Dirichlet problems. Inverse Probl. 32, 035007\u2013400 (2016)","journal-title":"Inverse Probl."},{"key":"1584_CR5","first-page":"1","volume":"99","author":"H Guo","year":"2017","unstructured":"Guo, H., Qi, J.: Extremal norm of potentials for Sturm\u2013Liouville eigenvalue problems with separated boundary conditions. Electron. J. Differ. Equ. 99, 1\u201311 (2017)","journal-title":"Electron. J. Differ. Equ."},{"key":"1584_CR6","first-page":"499","volume":"130","author":"R Kronig","year":"1931","unstructured":"Kronig, R., Penney, W.: Quantum mechanics in crystal lattices. Proc. R. Soc. Lond. 130, 499\u2013513 (1931)","journal-title":"Proc. R. Soc. Lond."},{"key":"1584_CR7","first-page":"761","volume":"31","author":"M Zhang","year":"2018","unstructured":"Zhang, M., Wen, Z., Meng, G., Qi, J., Xie, B.: On the number and complete continuity of weighted eigenvalues of measure differential equations. Differ. Integral Equ. 31, 761\u2013784 (2018)","journal-title":"Differ. Integral Equ."},{"key":"1584_CR8","first-page":"33","volume":"77A","author":"CT Fulton","year":"1977","unstructured":"Fulton, C.T.: Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions. Proc. Roy. Soc. Edingburg 77A, 33\u201342 (1977)","journal-title":"Proc. Roy. Soc. Edingburg"},{"key":"1584_CR9","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/BF01177870","volume":"133","author":"J Walter","year":"1973","unstructured":"Walter, J.: Regular eigenvalue problems with eigenvalue parameter in the boundary conditions. Mrth. Z. 133, 301\u2013312 (1973)","journal-title":"Mrth. Z."},{"key":"1584_CR10","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1017\/S0013091500018691","volume":"37","author":"PA Binding","year":"1993","unstructured":"Binding, P.A., Browne, P.J., Seddighi, K.: Sturm\u2013Liouville problems with eigenparameter dependent boundary conditions. Proc. Edin. Math. Soc. 37, 57\u201372 (1993)","journal-title":"Proc. Edin. Math. Soc."},{"key":"1584_CR11","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1016\/j.laa.2016.03.043","volume":"503","author":"C Gao","year":"2016","unstructured":"Gao, C., Ma, R.: Eigenvalues of discrete Sturm\u2013Liouville problems with eigenparameter dependent boundary conditions. Linear Algebra Appl. 503, 100\u2013119 (2016)","journal-title":"Linear Algebra Appl."},{"key":"1584_CR12","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1515\/9783110571622-014","volume-title":"Basic Theory","author":"Ricardo Almeida","year":"2019","unstructured":"Almeida, R., Torres, D.F.M.: A survey on fractional variational calculus. Handbook of Fractional Calculus with Applications, Vol 1: Basic Theory, De Gruyter, 347-360 (2019)"},{"key":"1584_CR13","doi-asserted-by":"publisher","DOI":"10.1142\/p871","volume-title":"Introduction to the Fractional Calculus of Variations","author":"AB Malinowska","year":"2012","unstructured":"Malinowska, A.B., Torres, D.F.M.: Introduction to the Fractional Calculus of Variations. Imperial College Press, London (2012)"},{"key":"1584_CR14","series-title":"Springer-Briefs in Applied Sciences and Technology","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-14756-7","volume-title":"Advanced Methods in the Fractional Calculus of Variations","author":"AB Malinowska","year":"2015","unstructured":"Malinowska, A.B., Torres, D.F.M.: Advanced Methods in the Fractional Calculus of Variations. Springer-Briefs in Applied Sciences and Technology. Springer, Cham (2015)"},{"key":"1584_CR15","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1016\/j.jmaa.2014.02.009","volume":"416","author":"M Klimek","year":"2014","unstructured":"Klimek, M., Odzijewicz, T., Malinowska, A.B.: Variational methods for the fractional Sturm\u2013Liouville problem. J. Math. Anal. Appl. 416, 402\u2013426 (2014)","journal-title":"J. Math. Anal. Appl."},{"key":"1584_CR16","first-page":"341","volume-title":"Discrete and Continuous Boundary Problems","author":"FV Atkinson","year":"1983","unstructured":"Atkinson, F.V.: Discrete and Continuous Boundary Problems, pp. 341\u2013355. Academic Press, New York (1983)"},{"key":"1584_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0070768","volume-title":"Volterra-Stieltjes Integral Equations and Generalized Ordinary Differential Expressions, 264\u2013279","author":"AB Mingarelli","year":"1983","unstructured":"Mingarelli, A.B.: Volterra-Stieltjes Integral Equations and Generalized Ordinary Differential Expressions, 264\u2013279. Springer, New York (1983)"},{"key":"1584_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6027-1","volume-title":"Linear Operators in Hilbert Spaces","author":"J Weidmann","year":"1980","unstructured":"Weidmann, J.: Linear Operators in Hilbert Spaces, vol. 107. Springer, New York (1980)"},{"key":"1584_CR19","volume-title":"Methods of Modern Mathematical Physics IV: Analysis of Operators","author":"M Reed","year":"2003","unstructured":"Reed, M., Simon, B.: Methods of Modern Mathematical Physics IV: Analysis of Operators. McGraw-Hill Book CO, Beijing (2003)"},{"key":"1584_CR20","doi-asserted-by":"crossref","unstructured":"Pinasco, J.P.: Lyapunov-type inequalities with application to eigenvalue problems, 4. Spinger Briefs in Mathematics (2013)","DOI":"10.1007\/978-1-4614-8523-0"},{"key":"1584_CR21","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1098\/rsta.1909.0016","volume":"209","author":"J Mercer","year":"1909","unstructured":"Mercer, J.: Functions of positive and negative type, and their connection with the theory of integral equations. Philos. Trans. Roy. Soc. London Ser. A. 209, 415\u2013446 (1909)","journal-title":"Philos. Trans. Roy. Soc. London Ser. A."},{"key":"1584_CR22","first-page":"245","volume-title":"Functional Analysis","author":"F Riesz","year":"1956","unstructured":"Riesz, F., Sz.-Nagy, B.: Functional Analysis, pp. 245\u2013246. Blackie & Limited, London and Glasgow (1956)"},{"key":"1584_CR23","doi-asserted-by":"publisher","first-page":"2196","DOI":"10.1016\/j.jde.2012.12.001","volume":"254","author":"G Meng","year":"2013","unstructured":"Meng, G., Zhang, M.: Dependence of solutions and eigenvalues of measure differential equations on measures. J. Differ. Equ. 254, 2196\u20132232 (2013)","journal-title":"J. Differ. Equ."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-019-01584-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-019-01584-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-019-01584-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,25]],"date-time":"2020-09-25T23:19:27Z","timestamp":1601075967000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-019-01584-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,27]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["1584"],"URL":"https:\/\/doi.org\/10.1007\/s10957-019-01584-x","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,9,27]]},"assertion":[{"value":"15 January 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 August 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 September 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}