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Upper and Lower Functions in Boundary Value Problems for a Third-Order Ordinary Differential Equation

Upper and Lower Functions in Boundary Value Problems for a Third-Order Ordinary Differential... Di erential Equations, Vol. 36, No. 12, 2000, pp. 1762{1769. Translated from Di erentsial'nye Uravneniya, Vol. 36, No. 12, 2000, pp. 1607{1614. Original Russian Text Copyright c 2000 by Klokov. ORDINARY DIFFERENTIAL EQUATIONS Upper and Lower Functions in Boundary Value Problems for a Third-Order Ordinary Di erential Equation Yu.A.Klokov Institute of Mathematics and Computer Science at Latvian University, Latvia Received October 30, 1999 The theory of upper and lower functions is well developed for boundary value problems for second-order di erential equations [1{5] but is yet to be created even for third-order equations. Some results in this direction were obtained in [6{8] and in the articles cited therein. 1. To clarify the diculties encountered here, we give some examples. Consider the boundary value problem x = f (t;x); (1) 0 0 x(0) = a;x (0) = a;x()= b ; (2) 0 1 1 where x 2 R, t 2 I =[0; ], I =(0; ), a ;a ;b 2 R, R =(−1; +1), R =[0;1), R =(−1; 0], 0 0 1 1 + − f 2 C (I  R), and the condition f (t;x)−H 8(t;x) 2 (I  R );f(t;x)  H 8(t;x) 2 (I  R)(A) + http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Upper and Lower Functions in Boundary Value Problems for a Third-Order Ordinary Differential Equation

Klokov, Yu.
Differential Equations , Volume 36 (12) – Oct 3, 2004
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References (1)

Publisher
Springer Journals
Copyright
Copyright © 2000 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1017540309727
Publisher site
See Article on Publisher Site

Abstract

Di erential Equations, Vol. 36, No. 12, 2000, pp. 1762{1769. Translated from Di erentsial'nye Uravneniya, Vol. 36, No. 12, 2000, pp. 1607{1614. Original Russian Text Copyright c 2000 by Klokov. ORDINARY DIFFERENTIAL EQUATIONS Upper and Lower Functions in Boundary Value Problems for a Third-Order Ordinary Di erential Equation Yu.A.Klokov Institute of Mathematics and Computer Science at Latvian University, Latvia Received October 30, 1999 The theory of upper and lower functions is well developed for boundary value problems for second-order di erential equations [1{5] but is yet to be created even for third-order equations. Some results in this direction were obtained in [6{8] and in the articles cited therein. 1. To clarify the diculties encountered here, we give some examples. Consider the boundary value problem x = f (t;x); (1) 0 0 x(0) = a;x (0) = a;x()= b ; (2) 0 1 1 where x 2 R, t 2 I =[0; ], I =(0; ), a ;a ;b 2 R, R =(−1; +1), R =[0;1), R =(−1; 0], 0 0 1 1 + − f 2 C (I  R), and the condition f (t;x)−H 8(t;x) 2 (I  R );f(t;x)  H 8(t;x) 2 (I  R)(A) +

Journal

Differential Equations – Springer Journals

Published: Oct 3, 2004

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