November  2005, 5(4): 1005-1014. doi: 10.3934/dcdsb.2005.5.1005

Existence of non-trivial nonnegative periodic solutions for a class of degenerate parabolic equations with nonlocal terms

1. 

Department of Mathematics, Jilin University, 130012 Changchun, China, China

2. 

Department of Mathematics, Beijing Institute of Technology, 100081 Beijing, China

Received  November 2004 Revised  April 2005 Published  August 2005

In this paper, we establish the existence of non-trivial nonnegative periodic solutions for a class of degenerate parabolic equations with nonlocal terms by using the theory of Leray-Schauder's degree.
Citation: Rui Huang, Yifu Wang, Yuanyuan Ke. Existence of non-trivial nonnegative periodic solutions for a class of degenerate parabolic equations with nonlocal terms. Discrete & Continuous Dynamical Systems - B, 2005, 5 (4) : 1005-1014. doi: 10.3934/dcdsb.2005.5.1005
[1]

Zalman Balanov, Meymanat Farzamirad, Wieslaw Krawcewicz, Haibo Ruan. Applied equivariant degree. part II: Symmetric Hopf bifurcations of functional differential equations. Discrete & Continuous Dynamical Systems - A, 2006, 16 (4) : 923-960. doi: 10.3934/dcds.2006.16.923

[2]

Lingwei Ma, Zhong Bo Fang. A new second critical exponent and life span for a quasilinear degenerate parabolic equation with weighted nonlocal sources. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1697-1706. doi: 10.3934/cpaa.2017081

[3]

Hermann J. Eberl, Messoud A. Efendiev, Dariusz Wrzosek, Anna Zhigun. Analysis of a degenerate biofilm model with a nutrient taxis term. Discrete & Continuous Dynamical Systems - A, 2014, 34 (1) : 99-119. doi: 10.3934/dcds.2014.34.99

[4]

Hui-Ling Li, Heng-Ling Wang, Xiao-Liu Wang. A quasilinear parabolic problem with a source term and a nonlocal absorption. Communications on Pure & Applied Analysis, 2018, 17 (5) : 1945-1956. doi: 10.3934/cpaa.2018092

[5]

Saugata Bandyopadhyay, Bernard Dacorogna, Olivier Kneuss. The Pullback equation for degenerate forms. Discrete & Continuous Dynamical Systems - A, 2010, 27 (2) : 657-691. doi: 10.3934/dcds.2010.27.657

[6]

Gisella Croce. An elliptic problem with degenerate coercivity and a singular quadratic gradient lower order term. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 507-530. doi: 10.3934/dcdss.2012.5.507

[7]

Min Chen, S. Dumont, Louis Dupaigne, Olivier Goubet. Decay of solutions to a water wave model with a nonlocal viscous dispersive term. Discrete & Continuous Dynamical Systems - A, 2010, 27 (4) : 1473-1492. doi: 10.3934/dcds.2010.27.1473

[8]

Luis Caffarelli, Serena Dipierro, Enrico Valdinoci. A logistic equation with nonlocal interactions. Kinetic & Related Models, 2017, 10 (1) : 141-170. doi: 10.3934/krm.2017006

[9]

Pablo Raúl Stinga, Chao Zhang. Harnack's inequality for fractional nonlocal equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 3153-3170. doi: 10.3934/dcds.2013.33.3153

[10]

Mourad Choulli, El Maati Ouhabaz, Masahiro Yamamoto. Stable determination of a semilinear term in a parabolic equation. Communications on Pure & Applied Analysis, 2006, 5 (3) : 447-462. doi: 10.3934/cpaa.2006.5.447

[11]

Bartosz Bieganowski, Simone Secchi. The semirelativistic Choquard equation with a local nonlinear term. Discrete & Continuous Dynamical Systems - A, 2019, 39 (7) : 4279-4302. doi: 10.3934/dcds.2019173

[12]

David Mumford, Peter W. Michor. On Euler's equation and 'EPDiff'. Journal of Geometric Mechanics, 2013, 5 (3) : 319-344. doi: 10.3934/jgm.2013.5.319

[13]

C. Brändle, E. Chasseigne, Raúl Ferreira. Unbounded solutions of the nonlocal heat equation. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1663-1686. doi: 10.3934/cpaa.2011.10.1663

[14]

Changfeng Gui, Zhenbu Zhang. Spike solutions to a nonlocal differential equation. Communications on Pure & Applied Analysis, 2006, 5 (1) : 85-95. doi: 10.3934/cpaa.2006.5.85

[15]

J. García-Melián, Julio D. Rossi. A logistic equation with refuge and nonlocal diffusion. Communications on Pure & Applied Analysis, 2009, 8 (6) : 2037-2053. doi: 10.3934/cpaa.2009.8.2037

[16]

Antonio Suárez. A logistic equation with degenerate diffusion and Robin boundary conditions. Communications on Pure & Applied Analysis, 2008, 7 (5) : 1255-1267. doi: 10.3934/cpaa.2008.7.1255

[17]

Andrea L. Bertozzi, Dejan Slepcev. Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion. Communications on Pure & Applied Analysis, 2010, 9 (6) : 1617-1637. doi: 10.3934/cpaa.2010.9.1617

[18]

Genggeng Huang. A Liouville theorem of degenerate elliptic equation and its application. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4549-4566. doi: 10.3934/dcds.2013.33.4549

[19]

Changchun Liu. A fourth order nonlinear degenerate parabolic equation. Communications on Pure & Applied Analysis, 2008, 7 (3) : 617-630. doi: 10.3934/cpaa.2008.7.617

[20]

Chi-Cheung Poon. Blowup rate of solutions of a degenerate nonlinear parabolic equation. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5317-5336. doi: 10.3934/dcdsb.2019060

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (12)

Other articles
by authors

[Back to Top]