Abstract
Existence results for semilinear systems of abstract evolution inclusions are established by means of Nadler, Bohnenblust-Karlin and Leray-Schauder fixed point theorems and a new technique for the treatment of systems based on vector-valued metrics and convergent to zero matrices.
Authors
Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Adrian Viorel
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Abstract parabolic evolution inclusion; parabolic system; initial value problem; fixed point theorem; vector-valued norm.
Paper coordinates
R. Precup, A. Viorel, Existence results for systems of nonlinear evolution inclusions, Fixed Point Theory 11 (2010) no. 2, 337-346.
About this paper
Journal
Fixed Point Theory
Publisher Name
DOI
Print ISSN
Online ISSN
??
google scholar link
[1] A. Bucur, L. Guran, A. Petru¸sel, Fixed points for multivalued operators on a set endowed with vector-valued metrics and applications, Fixed Point Theory 10(2009), 19-34.
[2] T. Cazenave, A. Haraux, An Introduction to Semilinear Evolution Equations, Oxford University Press, New York, 1998.
[3] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
[4] J.A. Goldstein, Semigroups of Linear Operators and Applications, Oxford University Press, New York, 1985.
[5] A. Granas, J. Dugudji, Fixed Point Theory, Springer, New York, 2003.
[6] J.M. Ortega, W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
[7] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, Berlin, 1983.
[8] R. Precup, The role of matrices that are convergent to zero in the study of semilinear operator systems, Math. Comp. Modelling, 49 (2009), 703-708.
[9] R. Precup, Methods in Nonlinear Integral Equations, Kluwer, Dordrecht, 2002.
[10] R. Precup, A. Viorel, Existence results for systems of nonlinear evolution equations, Int. J. Pure Appl. Math. IJPAM, 47(2008), No. 2, 199-206.
[11] F. Robert, Matrices non-negatives et normes vectorielles, Universit´e Scientifique et Medicale, Lyon, 1973.
[12] M.A. Serban, Fixed point theorems on Cartesian products, Fixed Point Theory, 9(2008), 331-350.
[13] I. Vrabie, C0-Semigroups and Applications, North-Holland, 2003.
[14] S. Zheng, Nonlinear Evolution Equations, Chapman & Hall/CRC, 2004