{"title":"Blow-up criteria of the simplified Ericksen–Leslie system","authors":"Zhen Chen, Fan Wu","doi":"10.1186/s13661-023-01729-y","DOIUrl":"https://doi.org/10.1186/s13661-023-01729-y","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-13"},"PeriodicalIF":1.7,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49634195","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}
{"title":"$(omega ,c)$-periodic solutions for a class of fractional integrodifferential equations","authors":"E. Alvarez, R. Grau, R. Meriño","doi":"10.1186/s13661-023-01726-1","DOIUrl":"https://doi.org/10.1186/s13661-023-01726-1","url":null,"abstract":"Abstract In this paper we investigate the following fractional order in time integrodifferential problem $$ mathbb{D}_{t}^{alpha}u(t)+Au(t)=f bigl(t,u(t) bigr)+ int _{-infty}^{t} k(t-s)g bigl(s,u(s) bigr),ds, quad t in mathbb{R}. $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>t</mml:mi> <mml:mi>α</mml:mi> </mml:msubsup> <mml:mi>u</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>+</mml:mo> <mml:mi>A</mml:mi> <mml:mi>u</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>u</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>+</mml:mo> <mml:msubsup> <mml:mo>∫</mml:mo> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> <mml:mi>t</mml:mi> </mml:msubsup> <mml:mi>k</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>−</mml:mo> <mml:mi>s</mml:mi> <mml:mo>)</mml:mo> <mml:mi>g</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>u</mml:mi> <mml:mo>(</mml:mo> <mml:mi>s</mml:mi> <mml:mo>)</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> <mml:mspace /> <mml:mi>d</mml:mi> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mspace /> <mml:mi>t</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>R</mml:mi> <mml:mo>.</mml:mo> </mml:math> Here, $mathbb{D}_{t}^{alpha}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>D</mml:mi> <mml:mi>t</mml:mi> <mml:mi>α</mml:mi> </mml:msubsup> </mml:math> is the Caputo derivative. We obtain results on the existence and uniqueness of $(omega ,c)$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>,</mml:mo> <mml:mi>c</mml:mi> <mml:mo>)</mml:mo> </mml:math> -periodic mild solutions assuming that − A generates an analytic semigroup on a Banach space X and f , g , and k satisfy suitable conditions. Finally, an interesting example that fits our framework is given.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135742747","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}
{"title":"A class of Schrödinger elliptic equations involving supercritical exponential growth","authors":"Y. R. S. Leuyacc","doi":"10.1186/s13661-023-01725-2","DOIUrl":"https://doi.org/10.1186/s13661-023-01725-2","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-17"},"PeriodicalIF":1.7,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47578184","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}
{"title":"Numerical solution of system of second-order integro-differential equations using nonclassical sinc collocation method","authors":"M. Ghasemi, Keivan Mohammadi, A. Alipanah","doi":"10.1186/s13661-023-01724-3","DOIUrl":"https://doi.org/10.1186/s13661-023-01724-3","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-24"},"PeriodicalIF":1.7,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46904030","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}
{"title":"Blow-up of solutions to the semilinear wave equation with scale invariant damping on exterior domain","authors":"Cui Ren, Sen Ming, Xiongmei Fan, Jiayi Du","doi":"10.1186/s13661-023-01722-5","DOIUrl":"https://doi.org/10.1186/s13661-023-01722-5","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"38 11","pages":"1-25"},"PeriodicalIF":1.7,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41293949","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}