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 and Continuous Dynamical Systems - B, 2005, 5 (4) : 1005-1014. doi: 10.3934/dcdsb.2005.5.1005
[1]

Abdelaaziz Sbai, Youssef El Hadfi, Mohammed Srati, Noureddine Aboutabit. Existence of solution for Kirchhoff type problem in Orlicz-Sobolev spaces Via Leray-Schauder's nonlinear alternative. Discrete and Continuous Dynamical Systems - S, 2022, 15 (1) : 213-227. doi: 10.3934/dcdss.2021015

[2]

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

[3]

Sergio Polidoro, Annalaura Rebucci, Bianca Stroffolini. Schauder type estimates for degenerate Kolmogorov equations with Dini continuous coefficients. Communications on Pure and Applied Analysis, 2022, 21 (4) : 1385-1416. doi: 10.3934/cpaa.2022023

[4]

Fedor Nazarov, Kevin Zumbrun. Instantaneous smoothing and exponential decay of solutions for a degenerate evolution equation with application to Boltzmann's equation. Kinetic and Related Models, 2022, 15 (4) : 729-752. doi: 10.3934/krm.2022012

[5]

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 and Applied Analysis, 2017, 16 (5) : 1697-1706. doi: 10.3934/cpaa.2017081

[6]

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

[7]

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

[8]

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

[9]

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

[10]

Gang Li, Fen Gu, Feida Jiang. Positive viscosity solutions of a third degree homogeneous parabolic infinity Laplace equation. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1449-1462. doi: 10.3934/cpaa.2020071

[11]

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

[12]

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

[13]

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

[14]

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

[15]

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

[16]

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

[17]

Françoise Demengel. Ergodic pairs for degenerate pseudo Pucci's fully nonlinear operators. Discrete and Continuous Dynamical Systems, 2021, 41 (7) : 3465-3488. doi: 10.3934/dcds.2021004

[18]

Henrik Garde, Nuutti Hyvönen. Reconstruction of singular and degenerate inclusions in Calderón's problem. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022021

[19]

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

[20]

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

2020 Impact Factor: 1.327

Metrics

  • PDF downloads (99)
  • HTML views (0)
  • Cited by (13)

Other articles
by authors

[Back to Top]