American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 376-385. doi: 10.3934/proc.2005.2005.376

Nonexistence of positive solutions of quasilinear elliptic equations with singularity on the boundary in strip-like domains

Takahiro Hashimoto 1,

1. 

Department of Mathematical Sciences, Faculty of Science, Ehime University, 2-5 Bunkyo-cho, Matsuyama-shi, Ehime, Japan 790-77, Japan

Received  September 2004 Revised  April 2005 Published  September 2005

In this paper, we discuss the nonexistence of positive solutions for nonlinear elliptic equations with singularity on the boundary in infinite strip-like domains. The main results are the nonexistence in eigen-value and sub principal case and they are shown by giving an argument concerning the simplicity of the first eigenvalue for generalized eigenvalue problems combined with translation invariance of the domain. We also show another nonexistence result via a modified version of Pohozaev-type identity.
Keywords: singularity., nonexistence, strip-like domains.
Mathematics Subject Classification: Primary: 35J20;Secondary: 35J7.
Citation: Takahiro Hashimoto. Nonexistence of positive solutions of quasilinear elliptic equations with singularity on the boundary in strip-like domains. Conference Publications, 2005, 2005 (Special) : 376-385. doi: 10.3934/proc.2005.2005.376
[1]

Takahiro Hashimoto, Mitsuharu Ôtani. Nonexistence of positive solutions for some quasilinear elliptic equations in strip-like domains. Discrete & Continuous Dynamical Systems, 1997, 3 (4) : 565-578. doi: 10.3934/dcds.1997.3.565
[2]

Alexandru Kristály, Ildikó-Ilona Mezei. Multiple solutions for a perturbed system on strip-like domains. Discrete & Continuous Dynamical Systems - S, 2012, 5 (4) : 789-796. doi: 10.3934/dcdss.2012.5.789
[3]

Luca Bisconti, Davide Catania. Global well-posedness of the two-dimensional horizontally filtered simplified Bardina turbulence model on a strip-like region. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1861-1881. doi: 10.3934/cpaa.2017090
[4]

Gennady G. Laptev. Some nonexistence results for higher-order evolution inequalities in cone-like domains. Electronic Research Announcements, 2001, 7: 87-93.

[5]

Yi Zhou, Jianli Liu. The initial-boundary value problem on a strip for the equation of time-like extremal surfaces. Discrete & Continuous Dynamical Systems, 2009, 23 (1&2) : 381-397. doi: 10.3934/dcds.2009.23.381
[6]

Teresa D'Aprile. Bubbling solutions for the Liouville equation around a quantized singularity in symmetric domains. Communications on Pure & Applied Analysis, 2021, 20 (1) : 159-191. doi: 10.3934/cpaa.2020262
[7]

Dario D. Monticelli, Fabio Punzo. Nonexistence results for elliptic differential inequalities with a potential in bounded domains. Discrete & Continuous Dynamical Systems, 2018, 38 (2) : 675-695. doi: 10.3934/dcds.2018029
[8]

Ilaria Fragalà, Filippo Gazzola, Gary Lieberman. Regularity and nonexistence results for anisotropic quasilinear elliptic equations in convex domains. Conference Publications, 2005, 2005 (Special) : 280-286. doi: 10.3934/proc.2005.2005.280
[9]

Marco Cabral, Ricardo Rosa, Roger Temam. Existence and dimension of the attractor for the Bénard problem on channel-like domains. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 89-116. doi: 10.3934/dcds.2004.10.89
[10]

Alexandre N. Carvalho, Jan W. Cholewa. NLS-like equations in bounded domains: Parabolic approximation procedure. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 57-77. doi: 10.3934/dcdsb.2018005
[11]

Takahiro Hashimoto. Nonexistence of global solutions of nonlinear Schrodinger equations in non star-shaped domains. Conference Publications, 2007, 2007 (Special) : 487-494. doi: 10.3934/proc.2007.2007.487
[12]

Xin-Guang Yang, Rong-Nian Wang, Xingjie Yan, Alain Miranville. Dynamics of the 2D Navier-Stokes equations with sublinear operators in Lipschitz-like domains. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3343-3366. doi: 10.3934/dcds.2020408
[13]

Zied Douzi, Bilel Selmi. On the mutual singularity of multifractal measures. Electronic Research Archive, 2020, 28 (1) : 423-432. doi: 10.3934/era.2020024
[14]

Henri Berestycki, Juncheng Wei. On least energy solutions to a semilinear elliptic equation in a strip. Discrete & Continuous Dynamical Systems, 2010, 28 (3) : 1083-1099. doi: 10.3934/dcds.2010.28.1083
[15]

Soumya Kundu, Soumitro Banerjee, Damian Giaouris. Vanishing singularity in hard impacting systems. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 319-332. doi: 10.3934/dcdsb.2011.16.319
[16]

Yimei Li, Jiguang Bao. Semilinear elliptic system with boundary singularity. Discrete & Continuous Dynamical Systems, 2020, 40 (4) : 2189-2212. doi: 10.3934/dcds.2020111
[17]

Lei Wei, Zhaosheng Feng. Isolated singularity for semilinear elliptic equations. Discrete & Continuous Dynamical Systems, 2015, 35 (7) : 3239-3252. doi: 10.3934/dcds.2015.35.3239
[18]

Michał Misiurewicz, Sonja Štimac. Lozi-like maps. Discrete & Continuous Dynamical Systems, 2018, 38 (6) : 2965-2985. doi: 10.3934/dcds.2018127
[19]

Sergei A. Nazarov, Rafael Orive-Illera, María-Eugenia Pérez-Martínez. Asymptotic structure of the spectrum in a Dirichlet-strip with double periodic perforations. Networks & Heterogeneous Media, 2019, 14 (4) : 733-757. doi: 10.3934/nhm.2019029
[20]

Peter Anthony, Sergey Zelik. Infinite-energy solutions for the Navier-Stokes equations in a strip revisited. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1361-1393. doi: 10.3934/cpaa.2014.13.1361

 Impact Factor: 

Tools

Metrics

  • PDF downloads (23)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy