{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,7]],"date-time":"2025-04-07T22:49:51Z","timestamp":1744066191286,"version":"3.28.0"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,12,7]],"date-time":"2023-12-07T00:00:00Z","timestamp":1701907200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,7]],"date-time":"2023-12-07T00:00:00Z","timestamp":1701907200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s10998-023-00562-1","type":"journal-article","created":{"date-parts":[[2023,12,7]],"date-time":"2023-12-07T05:02:01Z","timestamp":1701925321000},"page":"396-411","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A degenerate Kirchhoff-type problem involving variable $$s(\\cdot )$$-order fractional $$p(\\cdot )$$-Laplacian with weights"],"prefix":"10.1007","volume":"88","author":[{"given":"Mostafa","family":"Allaoui","sequence":"first","affiliation":[]},{"given":"Mohamed Karim","family":"Hamdani","sequence":"additional","affiliation":[]},{"given":"Lamine","family":"Mbarki","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,12,7]]},"reference":[{"key":"562_CR1","doi-asserted-by":"publisher","first-page":"1377","DOI":"10.1007\/s11785-018-00885-9","volume":"13","author":"KB Ali","year":"2019","unstructured":"K.B. Ali, M. Hsini, K. Kefi, N.T. Chung, On a nonlocal fractional $$p(.)$$-Laplacian problem with competing nonlinearities. Complex Anal. Oper. Theory. 13, 1377\u20131399 (2019)","journal-title":"Complex Anal. Oper. Theory."},{"key":"562_CR2","doi-asserted-by":"publisher","first-page":"1342","DOI":"10.55730\/1300-0098.3164","volume":"46","author":"R Ayazoglu","year":"2022","unstructured":"R. Ayazoglu, S. Akbulut, E. Akkoyunlu, Existence and multiplicity of solutions for $$p(.)$$-Kirchhoff-type equations. Turk. J. Math. 46, 1342\u20131359 (2022)","journal-title":"Turk. J. Math."},{"key":"562_CR3","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s13348-020-00283-5","volume":"72","author":"R Ayazoglu","year":"2021","unstructured":"R. Ayazoglu, Y. Sarac, S.S. Sener, G. Alisoy, Existence and multiplicity of solutions for a Schr\u00f6dinger-Kirchhoff type equation involving the fractional $$p(.)$$ -aplacian operator in $${\\mathbb{R} }^N$$. Collect. Math. 72, 129\u2013156 (2021)","journal-title":"Collect. Math."},{"key":"562_CR4","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1080\/00036811.2019.1603372","volume":"100","author":"E Azroul","year":"2021","unstructured":"E. Azroul, A. Benkirane, M. Shimi, M. Srati, On a class of fractional $$p(x)$$-Kirchhoff type. Appl. Anal. 100, 383\u2013402 (2021)","journal-title":"Appl. Anal."},{"key":"562_CR5","first-page":"379","volume":"11","author":"A Bahrouni","year":"2018","unstructured":"A. Bahrouni, V.D. R\u01cedulescu, On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent. Discrete Contin. Dyn. Syst. Ser. S. 11, 379\u2013389 (2018)","journal-title":"Discrete Contin. Dyn. Syst. Ser. S."},{"key":"562_CR6","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s00245-017-9458-5","volume":"80","author":"Z Binlin","year":"2019","unstructured":"Z. Binlin, A. Fiscella, S. Liang, Infinitely many solutions for critical degenerate Kirchhoff type equations involving the fractional p-Laplacian. Appl. Math. Optim. 80, 63\u201380 (2019)","journal-title":"Appl. Math. Optim."},{"key":"562_CR7","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1080\/17476933.2020.1751136","volume":"66","author":"R Biswas","year":"2021","unstructured":"R. Biswas, S. Tiwari, Variable order nonlocal Choquard problem with variable exponents. Complex Var. Elliptic Equ. 66, 853\u2013875 (2021)","journal-title":"Complex Var. Elliptic Equ."},{"key":"562_CR8","doi-asserted-by":"publisher","DOI":"10.1155\/2010\/120646","volume":"2010","author":"B Cekic","year":"2010","unstructured":"B. Cekic, R.A. Mashiyev, Existence and localization results for p(x)-Laplacian via topological methods. Fixed Point Theory Appl. 2010, 120646 (2010). https:\/\/doi.org\/10.1155\/2010\/120646","journal-title":"Fixed Point Theory Appl."},{"key":"562_CR9","volume-title":"Critical Point Theory and Applications","author":"KC Chang","year":"1986","unstructured":"K.C. Chang, Critical Point Theory and Applications (Shanghai Scientific and Technology Press, Shanghai, 1986)"},{"key":"562_CR10","doi-asserted-by":"crossref","first-page":"1153","DOI":"10.11650\/tjm\/190404","volume":"23","author":"NT Chung","year":"2019","unstructured":"N.T. Chung, Eigenvalue problems for fractional $$p(x, y)$$-Laplacian equations with indefinite weight. Taiwan. J. Math. 23, 1153\u20131173 (2019)","journal-title":"Taiwan. J. Math."},{"key":"562_CR11","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1512\/iumj.1973.22.22008","volume":"22","author":"DC Clarke","year":"1972","unstructured":"D.C. Clarke, A variant of the Lusternik\u2013Schnirelman theory. Indiana Univ. Math. J. 22, 65\u201374 (1972)","journal-title":"Indiana Univ. Math. J."},{"key":"562_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18363-8","volume-title":"Lebesgue and Sobolev Spaces with Variable Exponents, 2017","author":"L Diening","year":"2011","unstructured":"L. Diening, P. Harjulehto, P. H\u00e4st\u00f6, M. Ru\u017eicka, Lebesgue and Sobolev Spaces with Variable Exponents, 2017 (Springer, Heidelberg, 2011)"},{"key":"562_CR13","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1006\/jmaa.2000.7617","volume":"263","author":"X Fan","year":"2001","unstructured":"X. Fan, D. Zhao, On the spaces $$L^{p(x)}(\\Omega )$$ and $$W^{m, p(x)}(\\Omega )$$. J. Math. Anal. Appl. 263, 424\u2013446 (2001)","journal-title":"J. Math. Anal. Appl."},{"key":"562_CR14","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1016\/j.nonrwa.2016.11.004","volume":"35","author":"A Fiscella","year":"2017","unstructured":"A. Fiscella, P. Pucci, p-fractional Kirchhoff equations involving critical nonlinearities. Nonlinear Anal. Real World Appl. 35, 350\u2013378 (2017)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"562_CR15","first-page":"1","volume":"150","author":"MK Hamdani","year":"2020","unstructured":"M.K. Hamdani, J. Zuo, N.T. Chung, D.D. Repovs, Multiplicity of solutions for a class of fractional $$p(.)$$-Kirchhoff-type problems without the Ambrosetti\u2013Rabinowitz condition. Bound. Value Probl. 150, 1\u201316 (2020)","journal-title":"Bound. Value Probl."},{"key":"562_CR16","volume-title":"Topological Methods in the Theory of Nonlinear Integral Equations","author":"MA Krasnoselskii","year":"1964","unstructured":"M.A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations (MacMillan, New York, 1964)"},{"key":"562_CR17","doi-asserted-by":"publisher","first-page":"2721","DOI":"10.1002\/mma.6078","volume":"43","author":"M Massar","year":"2020","unstructured":"M. Massar, M. Talbi, On a class of p-fractional Laplacian equations with potential depending on parameter. Math. Methods Appl. Sci. 43, 2721\u20132734 (2020)","journal-title":"Math. Methods Appl. Sci."},{"key":"562_CR18","doi-asserted-by":"publisher","first-page":"2418","DOI":"10.1080\/00036811.2019.1688790","volume":"100","author":"L Wang","year":"2021","unstructured":"L. Wang, B. Zhang, Infinitely many solutions for Kirchhoff-type variable-order fractional Laplacian problems involving variable exponents. Appl. Anal. 100, 2418\u20132435 (2021)","journal-title":"Appl. Anal."},{"key":"562_CR19","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1016\/j.na.2018.07.016","volume":"178","author":"M Xiang","year":"2019","unstructured":"M. Xiang, B. Zhang, D. Yang, Multiplicity results for variable-order fractional Laplacian equations with variable growth. Nonlinear Anal. 178, 190\u2013204 (2019)","journal-title":"Nonlinear Anal."},{"key":"562_CR20","doi-asserted-by":"publisher","first-page":"1071","DOI":"10.1002\/mma.6813","volume":"44","author":"J Zuo","year":"2021","unstructured":"J. Zuo, T. An, A. Fiscella, A critical Kirchhoff-type problem driven by a $$p(.)$$- fractional Laplace operator with variable $$s(.)$$-order. Math. Methods Appl. Sci. 44, 1071\u20131085 (2021)","journal-title":"Math. Methods Appl. Sci."},{"key":"562_CR21","doi-asserted-by":"publisher","first-page":"3872","DOI":"10.1002\/mma.6995","volume":"44","author":"J Zuo","year":"2021","unstructured":"J. Zuo, L. Yang, S. Liang, A variable-order fractional $$p(.)$$-Kirchhoff type problem in $${\\mathbb{R} }^N$$. Math. Methods Appl. Sci. 44, 3872\u20133889 (2021)","journal-title":"Math. Methods Appl. Sci."},{"key":"562_CR22","doi-asserted-by":"publisher","first-page":"126264","DOI":"10.1016\/j.jmaa.2022.126264","volume":"514","author":"J Zuo","year":"2022","unstructured":"J. Zuo, D. Choudhuri, D.D. Repovs, On critical variable-order Kirchhoff type problems with variable singular exponent. J. Math. Anal. Appl. 514, 126264 (2022)","journal-title":"J. Math. Anal. Appl."},{"key":"562_CR23","doi-asserted-by":"publisher","first-page":"2532","DOI":"10.1007\/s13540-022-00105-4","volume":"25","author":"J Zuo","year":"2022","unstructured":"J. Zuo, D. Choudhuri, D.D. Repovs, Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents. Fract. Cal. Appl. Anal. 25, 2532\u20132553 (2022)","journal-title":"Fract. Cal. Appl. Anal."}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-023-00562-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10998-023-00562-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-023-00562-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,5]],"date-time":"2024-11-05T12:12:12Z","timestamp":1730808732000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10998-023-00562-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,7]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["562"],"URL":"https:\/\/doi.org\/10.1007\/s10998-023-00562-1","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"type":"print","value":"0031-5303"},{"type":"electronic","value":"1588-2829"}],"subject":[],"published":{"date-parts":[[2023,12,7]]},"assertion":[{"value":"20 July 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 December 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}