EXISTENCE OF POSITIVE SOLUTIONS OF A TERMINAL VALUE PROBLEM FOR SECOND ORDER DIFFERENTIAL EQUATIONS

TitleEXISTENCE OF POSITIVE SOLUTIONS OF A TERMINAL VALUE PROBLEM FOR SECOND ORDER DIFFERENTIAL EQUATIONS
Publication TypeJournal Article
Year of Publication2011
AuthorsMAVRIDIS, KYRIAKOS, TSAMATOS, PANAGIOTIS
Volume15
Issue4
Start Page539
Pagination8
Date Published2011
ISSN1083-2564
AMS34B18, 34B40, 34K10, 47H10
Abstract

In this paper we use the well–known Guo–Krasnoselskii fixed point theorem to establish conditions which guarantee the existence of at least one positive solution for a terminal value problem concerning a second order differential equation
URLhttp://www.acadsol.eu/en/articles/15/4/8.pdf
Refereed DesignationRefereed
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REFERENCES
[1] C. Avramescu, Sur l’ existence des solutions convergentes des systems d’ equations differentielles
non lineaires, Ann. Mat. Pura Appl. 81 (1969), 147–168.
[2] F. V. Atkinson, On second order nonlinear oscillation, Pacific J. Math. 5 (1955), 643–647.
[3] C. Bai and J. Fang, On positive solutions of boundary value problems for second order functional
differential equations on infinite intervals, J. Math. Anal. Appl. 282 (2003), 711–731.
[4] S. G. Dube and A. B. Mingarelli, Note on a non-oscillation theorem of Atkinson, Electron. J.Differential Equations 2004, No. 22, 6pp.
[5] D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, SanDiego, 1988.
[6] P. Hartman and A. Wintner, On the nonincreasing solutions of y′′ = f(x, y, y′), Amer. J.Math. 73 (1951), 390–404.
[7] E. Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948), 234–252
[8] M. A. Krasnoselskii, Positive solutions of Operator Equations, Noordhoff, Groningen, 1964.
[9] K. G. Mavridis, Ch. G. Philos and P. Ch. Tsamatos, Existence of solutions of a boundary
value problem on the half-line to second order nonlinear delay differential equations, Arch.
Math. (Basel) 86 (2006), No. 2, 163–175.
[10] Ch. G. Philos, I. K. Purnaras and P. Ch. Tsamatos, Global solutions approachinh lines at
infinity to second order nonlinear delay differential equations, Funkcialj Ekvacioj 50 (2007),213–259.
[11] W. E. Shreve, Terminal value problems for second order nonlineal differential equations, SIAM
J. Appl. Math. 18 (1970), No. 4, 783–791.
[12] E. Wahlen, Positive solutions of second–order differential equations, Nonlinear Anal. 58 (2004),359–366.
[13] P. K. Wong, Existence and asymptotic behavior of proper solutions of a class of second order
nonlinear differential equations, Pacific J. Math. 13 (1963), 737–760.
[14] B. Yan, Multiple unbounded solutions of boundary value problems for second-order differential
equations on the half-line, Nonlinear Anal. 51 (2002), 1031–1044.
[15] Z. Yin, Monotone positive solutions of the second order nonlinear differential equations, NonlinearAnal. 54 (2003), 391–403.