A version of Krasnosel'skiĭ's compression-expansion fixed point theorem in cones for discontinuous operators with applications
Keywords
Krasnosel'skiĭ fixed point theorem, positive solutions, discontinuous differential equationsAbstract
We introduce a new fixed point theorem of Krasnosel'skiĭ type for discontinuous operators. As an application we use it to study the existence of positive solutions of a second-order differential problem with separated boundary conditions and discontinuous nonlinearities.References
C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis. A Hitchhiker’s Guide, 3rd ed., Springer, 2006.
H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. 18 (1976), 620–709.
J.P. Aubin and A. Cellina, Differential Inclusions, Springer, 1984.
K. Deimling, Multivalued differential equations, Walter de Gruyter, Berlin, 1992.
L.H. Erbe, S. Hu and H. Wang, Multiple positive solutions of some boundary value problems, J. Math. Anal. Appl. 184 (1994), 640–648.
R. Figueroa and G. Infante, A Schauder-type theorem for discontinuous operators with applications to second-order BVPs, Fixed Point Theory Appl. 2016 (2016), Art. No. 57.
A. F. Filippov, Differential Equations with Discontinuous Righthand Sides, Kluwer Academic, Dordrecht, 1988.
P.M. Fitzpatrick and W.V. Petryshyn, Fixed point theorems and the fixed point index for multivalued mappings in cones, J. London Math. Soc. 2 (1975), no. 11, 75–85.
G. Infante, A short course on positive solutions of systems of ODEs via fixed point index, arXiv:1306.4875 [math.CA].
G. Infante and P. Pietramala, Nonzero radial solutions for a class of elliptic systems with nonlocal BCs on annular domains, Nonlinear Differential Equations Appl. 22 (2015), 979–1003.
K.Q. Lan, Multiple positive solutions of semilinear differential equations with singularities, J. London Math. Soc. 63 (2001), 690–704.
K.Q. Lan and J.R.L. Webb, Positive solutions of semilinear differential equations with singularities, J. Differential Equations 148 (1998), 407–421.
R. López Pouso, Schauder’s fixed-point theorem: new applications and a new version for discontinuous operators, Bound. Value Probl. 2012 (2012).
J.R.L. Webb, Positive solutions of some three point boundary value problems via fixed point index theory, Nonlinear Anal. 47 (2001), 4319–4332.
E. Zeidler, Nonlinear functional Analysis and its Applications I, Springer, New York, 1986.
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