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Basic Results in the Theory of Hybrid Casual Nonlinear Differential Equations
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  • Journal title : Kyungpook mathematical journal
  • Volume 55, Issue 4,  2015, pp.1069-1088
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2015.55.4.1069
 Title & Authors
Basic Results in the Theory of Hybrid Casual Nonlinear Differential Equations
DHAGE, BAPURAO CHANDRABHAN;
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 Abstract
In this paper, some basic results concerning the existence, strict and nonstrict inequalities and existence of the maximal and minimal solutions are proved for a hybrid causal differential equation. Our results generalize some basic results of Leela and Laksh-mikantham [13] and Dhage and Lakshmikantham [10] respectively for the nonlinear first order classical and hybrid differential equations.
 Keywords
Hybrid causal differential equation;Existence theorem;differential inequalities;Comparison result;Extremal solutions;
 Language
English
 Cited by
 References
1.
C. Corduneanu, Functional Equations with Causal Operators, Taylor and Francis, New York 2003.

2.
A.Granas, R. B. Guenther and J. W. Lee, Some general existence principles for Caratheodory theory of nonlinear differential equations, J. Math. Pures et Appl., 70(1991), 153-196.

3.
M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press 1964.

4.
T. A. Burton, A fixed point theorem of Krasnoselskii, Appl. Math. Lett., 11(1998), 83-88. crossref(new window)

5.
B. C. Dhage, A fixed point theorem in Banach algebras with applications to functional integral equations, Kyungpook Math. J., 44(2004), 145-155.

6.
B. C. Dhage, On ${\alpha}$-condensing mappings in Banach algebras, Mathematics Student, 63(1994), 146-152.

7.
B. C. Dhage, A nonlinear alternative in Banach algebras with applications to functional differential equations, Nonlinear Funct. Anal. & Appl., 8(2004), 563-575.

8.
B. C. Dhage, Fixed point theorems in ordered Banach algebras and applications, PanAmer. Math. J., 9(4)(1999), 93-102.

9.
B. C. Dhage, Quadratic perturbations of periodic boundary value problems of second order ordinary differential equations, Differ. Equ. Appl., 2(2010), 465-486.

10.
B. C. Dhage and V. Lakshmikantham, Basic results on hybrid differential equations, Nonlinear Analysis: Hybrid Systems, 4(2010), 414-424.

11.
Z. Drici, F. A. McRae and J. Vasundhara, Differential equations with causal operators in Banach spaces, Nonlinear Analysis, 62(2005), 301-313. crossref(new window)

12.
S. Heikkila and V. Lakshmikantham, Monotone Iterative Technique for Nonlinear Discontinues Differential Equations, Marcel Dekker Inc., New York, 1994.

13.
V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Academic Press, New York, 1969.