On-sided estimates for quasimonotone systems of boundary value problem

• Autorzy: Herzog G.
• Języki publikacji: EN

Abstrakty

EN

We prove existence and uniqueness theorems for Dirichlet boundary value problems of the form u" + f(t,u) = 0, u(0) = uo, u(1) = ui in ordered finite dimensional Banach spaces, involving one-sided estimates and quasimonotonicity.

Słowa kluczowe

EN

boundary value problem; Banach space; quasimonotone systems; differential inequalities; Dirichlet problem

PL

przestrzeń Banacha; zagadnienia brzegowe; nierówności różniczkowe; problem Dirichleta

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 4
• Strony: 847--856
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Herzog G.

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

Bibliografia

• [1] R. Dalmasso, Solutions of second order homogeneous Dirichlet systems. Hokkaido Math. J. 26 (1997), 611-630.
• [2] P. Hannig, Das Schießverfahren zur Gewinnung von Existenz und Eindeutigkeitsaussagen bei Sturm-Liouville-Randwertproblemen. Dissertation, Karlsruhe (1996).
• [3] P. Hartman, Ordinary Differential Equations. New York-London-Sydney: John Wiley and Sons, Inc. XIV, 612 p. (1964).
• [4] G. Herzog, One-sided estimates for linear quasimonotone increasing operators. Num. Funct. Anal. Opt. 19 (1998), 549-555.
• [5] G. Herzog, The Dirichlet problem for quasimonotone systems of second order equations. Rocky Mountain J. Math. 34 (2004), 195-204.
• [6] G. Herzog, R. Lemmert, An existence theorem for systems of boundary value problems. Proc. Am. Math. Soc. 128 (2000), 157-160.
• [7] G. Herzog, R. Lemmert, Second order differential inequalities in Banach spaces. Ann. Polon. Math. 77 (2001), 69-78.
• [8] G. Herzog, R. Lemmert, One-sided estimates for quasimonotone increasing functions. Bull. Australian Math. Soc. 67 (2003), 383-392.
• [9] M. A. Krasnoselski, A.I. Perow, A.I. Powolozki, P. P. Sabrejko, Vektorfelder in der Ebene. Mathematische Lehrbücher und Monographien, I. Abteilung, Bd. XIII. Berlin: Akademie-Verlag. X (1966).
• [10] M. Lees, Discrete methods for nonlinear two-point boundary value problems. Numer. Solution partial diff. Equations, Proc. Sympos. Univ. Maryland 1965, 59-72 (1966).
• [11] R. Lemmert, The shooting method for some nonlinear Sturm-Liouville boundary value problems. Z. Angew. Math. Phys. 40 (1989), 769-773.
• [12] R. H. Martin, Nonlinear Operators and Differential Equations in Banach spaces. Melbourne, Florida: Krieger Publishing Co., Inc. (1987).
• [13] J. Mawhin, Topological degree methods in nonlinear boundary value problems. Regional Conference Series in Mathematics. No.40. R.I.: The American Mathematical Society (AMS) (1979).
• [14] S. Mazur, Über konvexe Mengen in linearen normierten Räumen. Stud. Math. 4 (1933), 70-84.
• [15] M. Radulescu, S. Radulescu, An application of a global inversion theorem to a Dirichlet problem for a second order differential equation. Rev. Roum. Math. Pures Appl. 37 (1992), 929-933.
• [16] M. Radulescu, S. Radulescu, Global inversion theorem to unique solvability of Dirichlet problems. J. Math. Anal. Appl. 272 (2002), 362-367.
• [17] R. J. Stern, H. Wolkowicz, Exponential nonnegativity on the ice cream cone. SIAM J. Matrix Anal. Appl. 12 (1991), 160-165.
• [18] P. Volkmann, Gewöhnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen. Math. Z. 127 (1972), 157-164.