Semicontinuous solutions of systems of functional equations

• Autorzy: Herzog G.
• Języki publikacji: EN

Abstrakty

EN

We use the method of upper and lower solutions to prove the existence of upper and lower semicontinuous solutions of functional equations of the form F(w,u(w),u(g_1(w)),...,u(g_m(w)) = ) in R^n under monotonicity and quasimonotonicity assumptions on F, and for w from a metrizable topological spaces.

Słowa kluczowe

EN

functional equations; semicontinuous; upper solutions; lower solutions

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2003
• Tom: [Z] 43(2)
• Strony: 207--219
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Herzog G.

• Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany,

Bibliografia

• [1] K. Baron, Functional eąuations of infinite order, Prace Nauk. Uniw. Śląsk. 256, Katowice, 1978.
• [2] K. Baron, Note on the existence of continuous solutions of a functional equation of n-th order, Ann. Polon. Math. 30 (1974), 77-80.
• [3] K. Baron, M. Sablik, On the uniqueness of continuous solutions of a functional eąuation of n-th order, Aequationes Math. 17 (1978), 295-304.
• [4] B. Choczewski, R. Ger, M. Kuczma, Iterative Functional Equations, Cambridge University Press, Cambridge, 1990.
• [5] P. Hartman, Ordinary Differential Equations, Wiley Inc., New York 1964.
• [6] G. Herzog, A fixed point theorem for quasimonotone increasing mappings, Acta. Sci. Math. (Szeged) 64 (1998), 293-297.
• [7] G. Herzog, Quasimonotonicity, Nonlinear Analysis Th. Meth. Appl. 47 (2001), 2213-2224.
• [8] G. Herzog, R. Lemmert, Intermediate value theorems for quasimonotone increasing mappings, Numerical Funct. Anal. Opt. 20 (1999), 901-908.
• [9] S. Hu, Fixed points for discontinuous quasi-monotone maps in Rn, Proc. Amer. Math. Soc. 104 (1988), 1111-1114.
• [10] M. Kulawik, Continuous and semicontinuous solutions of a functional equation, Zeszyty Nauk. Politech Śląsk. Mat.-Fiz. 31 (1980), 65-77.
• [11] C. V. Pao, Nonlinear elliptic systems in unbounded domains, Nonlinear Analysis Th. Meth. Appl. 22 (1994), 1391-1407.
• [12] I. Redheffer, P. Volkmann, Ein Fixpunktsatz für quasimonoton wachsende Funktionen, Arch. Math. 70 (1998), 307-312.
• [13] S. Schmidt, Fixed points for discontinuous quasimonotone maps in sequence spaces, Proc. Amer. Math. Soc. 115 (1992), 361-363.
• [14] R. Uhl, Smallest and greatest fixed points of quasimonotone increasing mappings, Math. Nachr. 248/249 (2003), 204-210.
• [15] P. Volkmann, Gewöhnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen, Math. Z. 127 (1972), 157-164.