Pub Date : 2023-09-11DOI: 10.1186/s13661-023-01779-2
Mohamed Ben Ayed, Khalil El Mehdi
Abstract In this paper, we consider the Neumann elliptic problem $(mathcal{P}_{varepsilon})$ (Pε) : $-Delta u +mu u = u^{(({n+2})/({n-2}))+varepsilon}$ −Δu+μu=u((n+2)/(n−2))+ε , $u>0$ u>0 in Ω, ${partial u}/{partial nu}=0$ ∂u/∂ν=0 on ∂ Ω, where Ω is a smooth bounded domain in $mathbb{R}^{n}$ Rn , $ngeq 4$ n≥4 , ε is a small positive real, and μ is a fixed positive number. We show that, in contrast with the three dimensional case, $(mathcal{P}_{varepsilon})$ (Pε) has no solution blowing up at only interior points as ε goes to zero. The proof strategy consists in testing the equation by appropriate vector fields and then using refined asymptotic estimates in the neighborhood of bubbles, we obtain equilibrium conditions satisfied by the concentration parameters. The careful analysis of these balancing conditions allows us to obtain our results.
摘要本文考虑Neumann椭圆型问题$(mathcal{P}_{varepsilon})$ (P ε): $-Delta u +mu u = u^{(({n+2})/({n-2}))+varepsilon}$−Δ u + μ u = u ((n + 2) / (n−2))+ ε， $u>0$ u ＆gt;在Ω中为0,${partial u}/{partial nu}=0$∂u /∂ν = 0在∂Ω中，其中Ω是$mathbb{R}^{n}$ R n中的光滑有界域，$ngeq 4$ n≥4，ε是一个小的正实数，μ是一个固定的正数。我们证明，与三维情况相反，$(mathcal{P}_{varepsilon})$ (P ε)在ε趋于零时，没有解只在内部点爆炸。证明策略是利用适当的向量场对方程进行检验，然后利用气泡邻域的改进渐近估计，得到浓度参数满足的平衡条件。对这些平衡条件的仔细分析使我们得到了我们的结果。
{"title":"Nonexistence of interior bubbling solutions for slightly supercritical elliptic problems","authors":"Mohamed Ben Ayed, Khalil El Mehdi","doi":"10.1186/s13661-023-01779-2","DOIUrl":"https://doi.org/10.1186/s13661-023-01779-2","url":null,"abstract":"Abstract In this paper, we consider the Neumann elliptic problem $(mathcal{P}_{varepsilon})$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>ε</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:math> : $-Delta u +mu u = u^{(({n+2})/({n-2}))+varepsilon}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>−</mml:mo> <mml:mi>Δ</mml:mi> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mi>μ</mml:mi> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>u</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> <mml:mo>/</mml:mo> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> <mml:mo>)</mml:mo> <mml:mo>+</mml:mo> <mml:mi>ε</mml:mi> </mml:mrow> </mml:msup> </mml:math> , $u>0$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>u</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:math> in Ω, ${partial u}/{partial nu}=0$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>∂</mml:mi> <mml:mi>u</mml:mi> <mml:mo>/</mml:mo> <mml:mi>∂</mml:mi> <mml:mi>ν</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:math> on ∂ Ω, where Ω is a smooth bounded domain in $mathbb{R}^{n}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:math> , $ngeq 4$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>4</mml:mn> </mml:math> , ε is a small positive real, and μ is a fixed positive number. We show that, in contrast with the three dimensional case, $(mathcal{P}_{varepsilon})$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>ε</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:math> has no solution blowing up at only interior points as ε goes to zero. The proof strategy consists in testing the equation by appropriate vector fields and then using refined asymptotic estimates in the neighborhood of bubbles, we obtain equilibrium conditions satisfied by the concentration parameters. The careful analysis of these balancing conditions allows us to obtain our results.","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135980346","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 : 2023-08-31DOI: 10.1186/s13661-023-01774-7
G. Bonanno, G. D'Aguí, A. Sciammetta
{"title":"Multiple solutions for a class of anisotropic p⃗-Laplacian problems","authors":"G. Bonanno, G. D'Aguí, A. Sciammetta","doi":"10.1186/s13661-023-01774-7","DOIUrl":"https://doi.org/10.1186/s13661-023-01774-7","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-12"},"PeriodicalIF":1.7,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46834893","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 : 2023-08-30DOI: 10.1186/s13661-023-01777-4
Ning Wang, Zongfu Zhou
{"title":"Multiple positive solutions of fractional differential equations with improper integral boundary conditions on the half-line","authors":"Ning Wang, Zongfu Zhou","doi":"10.1186/s13661-023-01777-4","DOIUrl":"https://doi.org/10.1186/s13661-023-01777-4","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-17"},"PeriodicalIF":1.7,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45989882","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 : 2023-08-30DOI: 10.1186/s13661-023-01775-6
Y. Kan-on
{"title":"Short note on a solution with large amplitude for the limiting system arising from the competition-diffusion system","authors":"Y. Kan-on","doi":"10.1186/s13661-023-01775-6","DOIUrl":"https://doi.org/10.1186/s13661-023-01775-6","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-13"},"PeriodicalIF":1.7,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48470662","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 : 2023-08-28DOI: 10.1186/s13661-023-01776-5
Ziyue Cui, Zongfu Zhou
{"title":"Positive solutions for a class of fractional differential equations with infinite-point boundary conditions on infinite intervals","authors":"Ziyue Cui, Zongfu Zhou","doi":"10.1186/s13661-023-01776-5","DOIUrl":"https://doi.org/10.1186/s13661-023-01776-5","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-16"},"PeriodicalIF":1.7,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44595509","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 : 2023-08-28DOI: 10.1186/s13661-023-01752-z
Pallavi S. Scindia, Sanket Tikare, A. El-Deeb
{"title":"Ulam stability of first-order nonlinear impulsive dynamic equations","authors":"Pallavi S. Scindia, Sanket Tikare, A. El-Deeb","doi":"10.1186/s13661-023-01752-z","DOIUrl":"https://doi.org/10.1186/s13661-023-01752-z","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-13"},"PeriodicalIF":1.7,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45173896","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 : 2023-08-22DOI: 10.1186/s13661-023-01766-7
Yanmei Hu, W. Du
{"title":"Boundedness in a two-dimensional chemotaxis system with signal-dependent motility and logistic source","authors":"Yanmei Hu, W. Du","doi":"10.1186/s13661-023-01766-7","DOIUrl":"https://doi.org/10.1186/s13661-023-01766-7","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-22"},"PeriodicalIF":1.7,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48346849","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 : 2023-08-16DOI: 10.1186/s13661-023-01770-x
Zixin Liu, Wenfang Li, Changjin Xu, Chunfeng Liu, D. Mu, Mengzhu Xu, Wei-Bo Ou, Qing Cui
{"title":"Bifurcation mechanism and hybrid control strategy of a finance model with delays","authors":"Zixin Liu, Wenfang Li, Changjin Xu, Chunfeng Liu, D. Mu, Mengzhu Xu, Wei-Bo Ou, Qing Cui","doi":"10.1186/s13661-023-01770-x","DOIUrl":"https://doi.org/10.1186/s13661-023-01770-x","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-24"},"PeriodicalIF":1.7,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45328035","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 : 2023-08-16DOI: 10.1186/s13661-023-01771-w
M. S. Surendar, Muniagounder Sambath, K. Balachandran, Yongjuan Ma
{"title":"Qualitative analysis of a prey–predator model with prey refuge and intraspecific competition among predators","authors":"M. S. Surendar, Muniagounder Sambath, K. Balachandran, Yongjuan Ma","doi":"10.1186/s13661-023-01771-w","DOIUrl":"https://doi.org/10.1186/s13661-023-01771-w","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-21"},"PeriodicalIF":1.7,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45544130","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 : 2023-08-16DOI: 10.1186/s13661-023-01772-9
Siqi Xu
{"title":"A coupled complex mKdV equation and its N-soliton solutions via the Riemann–Hilbert approach","authors":"Siqi Xu","doi":"10.1186/s13661-023-01772-9","DOIUrl":"https://doi.org/10.1186/s13661-023-01772-9","url":null,"abstract":"","PeriodicalId":55333,"journal":{"name":"Boundary Value Problems","volume":" ","pages":"1-12"},"PeriodicalIF":1.7,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48486870","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：