Abstract
The existence of extremal fixed points for a family of increasing, not necessarily continuous, operators in ordered Banach spaces is achieved. The result is then employed to solve elliptic equations on the whole space with discontinuous nonlinearities.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Amann, Fixed points equations and nonlinear eigenvalue problems in ordered Banach spaces, Siam Rev. 18 (1976), 620–709.
E. Zeidler, Nonlinear Functional Analysis and its Applications I: Fixed-Point Theorems, Springer-Verlag, New York, 1986.
S. Heikkilä and V. Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Monographs Textbooks Pure Appl. Math. 181, Dekker, New York, 1994.
E. Liz, Monotone iterative techniques in ordered Banach spaces, Nonlinear Anal. 30 (1997), 5179–5190.
J.J. Nieto, An Abstract monotone iterative technique, Nonlinear Anal. 28 (1997), 1923–1933.
S. Heikkilä and S. Hu, On fixed points of multifunctions in ordered spaces, Appl. Anal. 51 (1993), 115–127.
G. Bonanno and S.A. Marano, Elliptic problems in IRn with discontinuous nonlinearities, Proc. Edinburgh Math. Soc., to appear.
J.M. Ball, Weak continuity properties of mappings and semigroups, Proc. Royal Soc. Edinburgh Sect. A 72 (1973/1974), 275–280.
O. Arino, S. Gauthier, and J.P. Penot, A fixed point theorem for sequentially continuous mappings with applications to ordinary differential equations, Funkcial. Ekvac. 27 (1984), 273–279.
C.A. Stuart, Bifurcation in Lp(IRn) for a semilinear elliptic equation, Proc. London Math. Soc. 57 (1988), 511–541.
R. Dautray and J.L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, vol. 1, Springer-Verlag, Berlin, 1990.
J. Appell, The superposition operator in function spaces — A survey, Expo. Math. 6 (1988), 209–270.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Kluwer Academic Publishers
About this chapter
Cite this chapter
Bonanno, G., Marano, S. (2001). Fixed Points in Ordered Banach Spaces and Applications to Elliptic Boundary-Value Problems. In: Giannessi, F., Maugeri, A., Pardalos, P.M. (eds) Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models. Nonconvex Optimization and Its Applications, vol 58. Springer, Boston, MA. https://doi.org/10.1007/0-306-48026-3_2
Download citation
DOI: https://doi.org/10.1007/0-306-48026-3_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4020-0161-1
Online ISBN: 978-0-306-48026-3
eBook Packages: Springer Book Archive