Second order differential inequalities via aggregation

• Autorzy: Herzog G. , Lemmert R.
• Języki publikacji: EN

Abstrakty

EN

Let E be a Banach space ordered by a solid and normal cone. We introduce a polynorm with respect to a given selection of positive pairwise disjoint vectors p1, . . . , pm, and derive monotonicity properties of solutions of second order differential inequalities under one-sided matrix Lipschitz conditions.

Słowa kluczowe

EN

differential inequalities; ordered Banach spaces; quasimonotone increasing functions; boundary value problem

PL

nierówności różniczkowe; uporządkowana przestrzeń Banacha; funkcje quasimonotoniczne; zagadnienie brzegowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 2
• Strony: 347--364
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Herzog G.

autor

Lemmert R.

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

Bibliografia

• [1] G. Herzog, The Dirichlet problem for quasimonotone systems of second order equations Rocky Mountain J. Math. 34 (2004), 195-204.
• [2] G. Herzog, R. Lemmert, On ordered spaces of polynomials, Linear Algebra Appl. 320 (2000), 199-203.
• [3] G. Herzog, R. Lemmert, Second order differential inequalities in Banach spaces, Ann. Polon. Math. 77 (2001), 69-78.
• [4] G. Herzog, R. Lemmert, One-sided estimates for quasimonotone increasing functions, Bull. Austral. Math. Soc. 67 (2003), 383-392.
• [5] G. Herzog, R. Lemmert, On BVPs in l1(A), Extracta Math. 20 (2005), 13-23.
• [6] R. H. Martin, Nonlinear Operators and Differential Equations in Banach spaces, Robert E. Krieger Publ. Company, Malabar, 1987.
• [7] S. Mazur, Über konvexe Mengen in linearen normierten Räumen, Stud. Math. 4 (1933), 70-84.
• [8] H. L. Smith, A note on disconjugacy for second order systems, Pacific J. Math. 89 (1980), 447-452.
• [9] R. Uhl, Ordinary differential inequalities and quasimonotonicity in ordered topological vector spaces, Proc. Amer. Math. Soc. 126 (1998), 1999-2003.
• [10] P. Volkmann, Gewöhnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen, Math. Z. 127 (1972), 157-164.