Abstract
In this chapter we shall consider two systems of integral equations, one is on a finite interval
and the other is on the half-line [0,∞)
In both (6.1.1) and (6.1.2), μ is a positive number, the function f may take negative values, and \(f(\cdot,u_{1},u_{2},\cdots \,,u_{n})\) may be singular at u j = 0, \(j \in \{ 1,2,\cdots \,,n\}.\)
Keywords
- Semipositone
- Singular Integral Equations
- Negative Values
- Constant Sign Solutions
- Chemical Reactor Theory
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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R.P. Agarwal, S.R. Grace, D. O’Regan, Existence of positive solutions to semipositone Fredholm integral equations. Funkcial. Ekvac. 45, 223–235 (2002)
R.P. Agarwal, D. O’Regan, Singular differential, integral and discrete equations: the semipositone case. Mosc. Math. J. 2, 1–15 (2002)
R.P. Agarwal, D. O’Regan, P.J.Y. Wong, Positive Solutions of Differential, Difference and Integral Equations (Kluwer, Dordrecht, 1999)
R.P. Agarwal, D. O’Regan, P.J.Y. Wong, Constant-sign solutions of a system of integral equations: the semipositone and singular case. Asymptot. Anal. 43, 47–74 (2005)
P.W. Eloe, J. Henderson, Singular nonlinear (k,n − k) conjugate boundary value problems. J. Differ. Equat. 133, 136–151 (1997)
L.H. Erbe, S. Hu, H. Wang, Multiple positive solutions of some boundary value problems. J. Math. Anal. Appl. 184, 640–648 (1994)
L.H. Erbe, H. Wang, On the existence of positive solutions of ordinary differential equations. Proc. Am. Math. Soc. 120, 743–748 (1994)
C.P. Gupta, Existence and uniqueness theorems for the bending of an elastic beam equation. Appl. Anal. 26, 289–304 (1998)
W. Lian, F. Wong, C. Yeh, On the existence of positive solutions of nonlinear second order differential equations. Proc. Am. Math. Soc. 124, 1117–1126 (1996)
D. O’Regan, M. Meehan, Existence Theory for Nonlinear Integral and Integrodifferential Equations (Kluwer, Dordrecht, 1998)
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Agarwal, R.P., O’Regan, D., Wong, P.J.Y. (2013). System of Fredholm Integral Equations: Semipositone and Singular Case. In: Constant-Sign Solutions of Systems of Integral Equations. Springer, Cham. https://doi.org/10.1007/978-3-319-01255-1_6
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DOI: https://doi.org/10.1007/978-3-319-01255-1_6
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