Pub Date : 2023-04-04DOI: 10.1186/s13661-023-01719-0
Changmu Chu, Zhongju He
Abstract In this paper, we study the existence of a class of $p(x)$ p(x) -Kirchhoff equation involving concave-convex nonlinearities. The main tools used are the perturbation technique, variational method, and a priori estimation.
{"title":"Nonnegative nontrivial solutions for a class of $p(x)$-Kirchhoff equation involving concave-convex nonlinearities","authors":"Changmu Chu, Zhongju He","doi":"10.1186/s13661-023-01719-0","DOIUrl":"https://doi.org/10.1186/s13661-023-01719-0","url":null,"abstract":"Abstract In this paper, we study the existence of a class of $p(x)$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>p</mml:mi> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> </mml:math> -Kirchhoff equation involving concave-convex nonlinearities. The main tools used are the perturbation technique, variational method, and a priori estimation.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136188999","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 : 2023-04-01DOI: 10.1186/s13661-023-01717-2
Xingtian Gong, Shuwei Yang
{"title":"A local regularization scheme of Cauchy problem for the Laplace equation on a doubly connected domain","authors":"Xingtian Gong, Shuwei Yang","doi":"10.1186/s13661-023-01717-2","DOIUrl":"https://doi.org/10.1186/s13661-023-01717-2","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49047211","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 : 2023-03-31DOI: 10.1186/s13661-023-01720-7
Yongxin Jiang, W. Shi, Xiaojuan Li
{"title":"Existence theory for multiple solutions to second-order singular Dirichlet boundary value problem modeling the Antarctic Circumpolar Current","authors":"Yongxin Jiang, W. Shi, Xiaojuan Li","doi":"10.1186/s13661-023-01720-7","DOIUrl":"https://doi.org/10.1186/s13661-023-01720-7","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43365071","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 : 2023-03-31DOI: 10.1186/s13661-023-01723-4
Baoying Du
Abstract In this paper, we investigate the 3D incompressible Hall-magnetohydrodynamics with partial dissipation. Based on the results in (Du in Bound. Value Probl. 2022:6, 2022; Du and Liu in Acta Math. Sci. 42A:5, 2022; Fei and Xiang in J. Math. Phys. 56:051504, 2015), we establish an improved blow-up criterion for classical solutions. Furthermore, using the blow-up criterion, we also obtain the existence of the classical solutions only under the condition that the initial data $|V_{0}|_{H^{1}}+|B_{0}|_{H^{2}}$ ∥V0∥H1+∥B0∥H2 are sufficiently small.
{"title":"On the blow-up criterion for the Hall-MHD problem with partial dissipation in $mathbb{R}^{3}$","authors":"Baoying Du","doi":"10.1186/s13661-023-01723-4","DOIUrl":"https://doi.org/10.1186/s13661-023-01723-4","url":null,"abstract":"Abstract In this paper, we investigate the 3D incompressible Hall-magnetohydrodynamics with partial dissipation. Based on the results in (Du in Bound. Value Probl. 2022:6, 2022; Du and Liu in Acta Math. Sci. 42A:5, 2022; Fei and Xiang in J. Math. Phys. 56:051504, 2015), we establish an improved blow-up criterion for classical solutions. Furthermore, using the blow-up criterion, we also obtain the existence of the classical solutions only under the condition that the initial data $|V_{0}|_{H^{1}}+|B_{0}|_{H^{2}}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mrow> <mml:mo>∥</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>∥</mml:mo> </mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:msub> <mml:mo>+</mml:mo> <mml:msub> <mml:mrow> <mml:mo>∥</mml:mo> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>∥</mml:mo> </mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:msub> </mml:math> are sufficiently small.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135788031","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 : 2023-03-30DOI: 10.1186/s13661-023-01721-6
T. Saanouni, S. Boulaaras, Congming Peng
{"title":"A note on inhomogeneous fractional Schrödinger equations","authors":"T. Saanouni, S. Boulaaras, Congming Peng","doi":"10.1186/s13661-023-01721-6","DOIUrl":"https://doi.org/10.1186/s13661-023-01721-6","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49543148","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 : 2023-03-29DOI: 10.1186/s13661-023-01707-4
Erbil Çetin, F. Topal, R. Agarwal
{"title":"Existence of positive solutions for Lidstone boundary value problems on time scales","authors":"Erbil Çetin, F. Topal, R. Agarwal","doi":"10.1186/s13661-023-01707-4","DOIUrl":"https://doi.org/10.1186/s13661-023-01707-4","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47730307","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 : 2023-03-22DOI: 10.1186/s13661-023-01714-5
W. Shi
{"title":"Nonexistence results of solutions of parabolic-type equations and systems on the Heisenberg group","authors":"W. Shi","doi":"10.1186/s13661-023-01714-5","DOIUrl":"https://doi.org/10.1186/s13661-023-01714-5","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42622401","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 : 2023-03-21DOI: 10.1186/s13661-023-01716-3
Miao Liu, Jiangang Tang, S. Lai
{"title":"A necessary and sufficient condition of blow-up for a nonlinear equation","authors":"Miao Liu, Jiangang Tang, S. Lai","doi":"10.1186/s13661-023-01716-3","DOIUrl":"https://doi.org/10.1186/s13661-023-01716-3","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44073314","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 : 2023-03-17DOI: 10.1186/s13661-023-01715-4
Xiaobin Yao
{"title":"Asymptotic behavior of plate equations driven by colored noise on unbounded domains","authors":"Xiaobin Yao","doi":"10.1186/s13661-023-01715-4","DOIUrl":"https://doi.org/10.1186/s13661-023-01715-4","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41633705","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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