American Institute of Mathematical Sciences

Advanced
2009, 2009(Special): 82-91. doi: 10.3934/proc.2009.2009.82

Nonlocal problems for parabolic inclusions

Abdelkader Boucherif 1,

1. 

Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Box 5046 Dhahran, 31261

Received  June 2008 Revised  April 2009 Published  September 2009

In this paper we investigate a class of parabolic inclusions with a nonlocal condition of integral type. We provide sufficient conditions that guarantee the existence of at least one solution. Our technique is based on Green's function for linear parabolic partial differential equations and fixed point theorems for multivalued maps.
Keywords: parabolic problems; integral representation of solutions, multivalued maps, nonlocal conditions, fixed point theorems.
Mathematics Subject Classification: Primary: 35R70; Secondary:35K60; 35C15.
Citation: Abdelkader Boucherif. Nonlocal problems for parabolic inclusions. Conference Publications, 2009, 2009 (Special) : 82-91. doi: 10.3934/proc.2009.2009.82
[1]

Parin Chaipunya, Poom Kumam. Fixed point theorems for cyclic operators with application in Fractional integral inclusions with delays. Conference Publications, 2015, 2015 (special) : 248-257. doi: 10.3934/proc.2015.0248
[2]

Tiziana Cardinali, Paola Rubbioni. Existence theorems for generalized nonlinear quadratic integral equations via a new fixed point result. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020152
[3]

Yakov Krasnov, Alexander Kononovich, Grigory Osharovich. On a structure of the fixed point set of homogeneous maps. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 1017-1027. doi: 10.3934/dcdss.2013.6.1017
[4]

Luis Hernández-Corbato, Francisco R. Ruiz del Portal. Fixed point indices of planar continuous maps. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 2979-2995. doi: 10.3934/dcds.2015.35.2979
[5]

Teck-Cheong Lim. On the largest common fixed point of a commuting family of isotone maps. Conference Publications, 2005, 2005 (Special) : 621-623. doi: 10.3934/proc.2005.2005.621
[6]

Grzegorz Graff, Piotr Nowak-Przygodzki. Fixed point indices of iterations of $C^1$ maps in $R^3$. Discrete & Continuous Dynamical Systems - A, 2006, 16 (4) : 843-856. doi: 10.3934/dcds.2006.16.843
[7]

Romain Aimino, Huyi Hu, Matthew Nicol, Andrei Török, Sandro Vaienti. Polynomial loss of memory for maps of the interval with a neutral fixed point. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 793-806. doi: 10.3934/dcds.2015.35.793
[8]

Stanislav Antontsev, Michel Chipot, Sergey Shmarev. Uniqueness and comparison theorems for solutions of doubly nonlinear parabolic equations with nonstandard growth conditions. Communications on Pure & Applied Analysis, 2013, 12 (4) : 1527-1546. doi: 10.3934/cpaa.2013.12.1527
[9]

Davide Guidetti. Classical solutions to quasilinear parabolic problems with dynamic boundary conditions. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 717-736. doi: 10.3934/dcdss.2016024
[10]

Paolo Perfetti. Fixed point theorems in the Arnol'd model about instability of the action-variables in phase-space. Discrete & Continuous Dynamical Systems - A, 1998, 4 (2) : 379-391. doi: 10.3934/dcds.1998.4.379
[11]

Mircea Sofonea, Cezar Avramescu, Andaluzia Matei. A fixed point result with applications in the study of viscoplastic frictionless contact problems. Communications on Pure & Applied Analysis, 2008, 7 (3) : 645-658. doi: 10.3934/cpaa.2008.7.645
[12]

Olexiy V. Kapustyan, Pavlo O. Kasyanov, José Valero, Mikhail Z. Zgurovsky. Attractors of multivalued semi-flows generated by solutions of optimal control problems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1229-1242. doi: 10.3934/dcdsb.2019013
[13]

Irene Benedetti, Valeri Obukhovskii, Valentina Taddei. Evolution fractional differential problems with impulses and nonlocal conditions. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020149
[14]

Gary Lieberman. Nonlocal problems for quasilinear parabolic equations in divergence form. Conference Publications, 2003, 2003 (Special) : 563-570. doi: 10.3934/proc.2003.2003.563
[15]

Alexandre Nolasco de Carvalho, Marcos Roberto Teixeira Primo. Spatial homogeneity in parabolic problems with nonlinear boundary conditions. Communications on Pure & Applied Analysis, 2004, 3 (4) : 637-651. doi: 10.3934/cpaa.2004.3.637
[16]

Nicholas Long. Fixed point shifts of inert involutions. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1297-1317. doi: 10.3934/dcds.2009.25.1297
[17]

Kanghui Guo and Demetrio Labate. Sparse shearlet representation of Fourier integral operators. Electronic Research Announcements, 2007, 14: 7-19. doi: 10.3934/era.2007.14.7
[18]

Joshua Du, Jun Ji. An integral representation of the determinant of a matrix and its applications. Conference Publications, 2005, 2005 (Special) : 225-232. doi: 10.3934/proc.2005.2005.225
[19]

Gennaro Infante. Eigenvalues and positive solutions of odes involving integral boundary conditions. Conference Publications, 2005, 2005 (Special) : 436-442. doi: 10.3934/proc.2005.2005.436
[20]

Abdelkader Boucherif. Positive Solutions of second order differential equations with integral boundary conditions. Conference Publications, 2007, 2007 (Special) : 155-159. doi: 10.3934/proc.2007.2007.155

 Impact Factor: 

Tools

Metrics

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

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences