Pub Date : 2023-12-01DOI: 10.1216/rmj.2023.53.1847
Guodong Hua
{"title":"THE THREE-DIMENSIONAL DIVISOR PROBLEMS RELATED TO CUSP FORM COEFFICIENTS","authors":"Guodong Hua","doi":"10.1216/rmj.2023.53.1847","DOIUrl":"https://doi.org/10.1216/rmj.2023.53.1847","url":null,"abstract":"","PeriodicalId":49591,"journal":{"name":"Rocky Mountain Journal of Mathematics","volume":"62 6","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139012719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-01DOI: 10.1216/rmj.2023.53.1817
Amouria Hammou, S. Hamani, Johnny Henderson
{"title":"UPPER AND LOWER SOLUTION METHODS FOR IMPULSIVE CAPUTO–HADAMARD FRACTIONAL DIFFERENTIAL INCLUSIONS","authors":"Amouria Hammou, S. Hamani, Johnny Henderson","doi":"10.1216/rmj.2023.53.1817","DOIUrl":"https://doi.org/10.1216/rmj.2023.53.1817","url":null,"abstract":"","PeriodicalId":49591,"journal":{"name":"Rocky Mountain Journal of Mathematics","volume":"51 ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139017998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-01DOI: 10.1216/rmj.2023.53.1997
{"title":"Author Index for Volume 53 (2023)","authors":"","doi":"10.1216/rmj.2023.53.1997","DOIUrl":"https://doi.org/10.1216/rmj.2023.53.1997","url":null,"abstract":"","PeriodicalId":49591,"journal":{"name":"Rocky Mountain Journal of Mathematics","volume":"877 10","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139019752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-01DOI: 10.1216/rmj.2023.53.1767
Haniye Dehestani, Y. Ordokhani
{"title":"AN ACCURATE NUMERICAL ALGORITHM TO INVESTIGATE THE SOLUTION OF FRACTAL-FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS","authors":"Haniye Dehestani, Y. Ordokhani","doi":"10.1216/rmj.2023.53.1767","DOIUrl":"https://doi.org/10.1216/rmj.2023.53.1767","url":null,"abstract":"","PeriodicalId":49591,"journal":{"name":"Rocky Mountain Journal of Mathematics","volume":"38 ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139023284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-01DOI: 10.1216/rmj.2023.53.1965
Parul Saini, Ü. Çakan, Amar Deep
{"title":"EXISTENCE OF SOLUTIONS FOR 2D NONLINEAR FRACTIONAL VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACE","authors":"Parul Saini, Ü. Çakan, Amar Deep","doi":"10.1216/rmj.2023.53.1965","DOIUrl":"https://doi.org/10.1216/rmj.2023.53.1965","url":null,"abstract":"","PeriodicalId":49591,"journal":{"name":"Rocky Mountain Journal of Mathematics","volume":"91 8","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139025273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1216/rmj.2023.53.1609
Guoru Wang, Feng Liu
We introduce and study the regularity properties of the commutator of the bilinear maximal operator and the bilinear maximal commutator. We establish some new bounds for the weak gradient of the above commutators. We also obtain the boundedness and continuity of the above commutators on the Triebel–Lizorkin spaces and Besov spaces.
{"title":"REGULARITY OF COMMUTATORS OF THE BILINEAR MAXIMAL OPERATOR","authors":"Guoru Wang, Feng Liu","doi":"10.1216/rmj.2023.53.1609","DOIUrl":"https://doi.org/10.1216/rmj.2023.53.1609","url":null,"abstract":"We introduce and study the regularity properties of the commutator of the bilinear maximal operator and the bilinear maximal commutator. We establish some new bounds for the weak gradient of the above commutators. We also obtain the boundedness and continuity of the above commutators on the Triebel–Lizorkin spaces and Besov spaces.","PeriodicalId":49591,"journal":{"name":"Rocky Mountain Journal of Mathematics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135323138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1216/rmj.2023.53.1525
Ruyun Ma, Yali Zhang
We show the global structure of positive solutions for second order periodic boundary value problem { −Δ2u(t−1)=λa(t)g(u(t)), t∈ℕ1T,u(0)=u(T), u(1)=u(T+1), where ℕ1T={1,2,…,T},T≥3 is an integer, λ>0 is a parameter, g:[0,∞)→[0,∞) is a continuous function with g(0)=0 and a:ℕ1T→ℝ is sign-changing. Depending on the behavior of g near 0 and ∞, we obtain that there exist 0<λ0≤λ1 such that above problem has at least two positive solutions for λ>λ1 and no solution for λ∈(0,λ0). The proof of our main results is based upon bifurcation technique.
给出了二阶周期边值问题{−Δ2u(t−1)=λa(t)g(u(t))的正解的整体结构，其中，t∈∈n = t,u(0)=u(t)，u(1)=u(t +1)，其中，n ={1,2，…，t}， t≥3是整数，λ>0是参数，g:[0，∞)→[0，∞)是连续函数，g(0)=0, a: n = n→t是变号函数。根据g在0和∞附近的行为，我们得到了λ∈(0，λ0)存在0λ1且无解。我们的主要结果的证明是基于分岔技术。
{"title":"GLOBAL STRUCTURE OF POSITIVE SOLUTIONS FOR SECOND ORDER DISCRETE PERIODIC BOUNDARY VALUE PROBLEM WITH INDEFINITE WEIGHT","authors":"Ruyun Ma, Yali Zhang","doi":"10.1216/rmj.2023.53.1525","DOIUrl":"https://doi.org/10.1216/rmj.2023.53.1525","url":null,"abstract":"We show the global structure of positive solutions for second order periodic boundary value problem { −Δ2u(t−1)=λa(t)g(u(t)), t∈ℕ1T,u(0)=u(T), u(1)=u(T+1), where ℕ1T={1,2,…,T},T≥3 is an integer, λ>0 is a parameter, g:[0,∞)→[0,∞) is a continuous function with g(0)=0 and a:ℕ1T→ℝ is sign-changing. Depending on the behavior of g near 0 and ∞, we obtain that there exist 0<λ0≤λ1 such that above problem has at least two positive solutions for λ>λ1 and no solution for λ∈(0,λ0). The proof of our main results is based upon bifurcation technique.","PeriodicalId":49591,"journal":{"name":"Rocky Mountain Journal of Mathematics","volume":"277 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135323139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1216/rmj.2023.53.1431
Tianlan Chen, Yali Zhao
We show some existence results for the system of nonlocal Neumann problems with the Minkowski-curvature operator (rN−1u′1−u′2)′=rN−1f(r,u,u′), r∈(0,1), u′(0)=0, u′(1)=∫01u′(s)dg(s), where N≥1 is an integer, f:[0,1]×ℝk×Ik→ℝk is continuous and bounded, I≔(−1,1), and g:[0,1]→ℝk is a function of bounded variation. The proof is based on topological-degree arguments and extends to a larger class of nonlinearities.
{"title":"EXISTENCE OF SOLUTIONS FOR SYSTEMS OF MINKOWSKI-CURVATURE NEUMANN PROBLEMS","authors":"Tianlan Chen, Yali Zhao","doi":"10.1216/rmj.2023.53.1431","DOIUrl":"https://doi.org/10.1216/rmj.2023.53.1431","url":null,"abstract":"We show some existence results for the system of nonlocal Neumann problems with the Minkowski-curvature operator (rN−1u′1−u′2)′=rN−1f(r,u,u′), r∈(0,1), u′(0)=0, u′(1)=∫01u′(s)dg(s), where N≥1 is an integer, f:[0,1]×ℝk×Ik→ℝk is continuous and bounded, I≔(−1,1), and g:[0,1]→ℝk is a function of bounded variation. The proof is based on topological-degree arguments and extends to a larger class of nonlinearities.","PeriodicalId":49591,"journal":{"name":"Rocky Mountain Journal of Mathematics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135323333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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