Existence of solutions for threepoint boundary value problems for second order equations
Authors:
Johnny Henderson, Basant Karna and Christopher C. Tisdell
Journal:
Proc. Amer. Math. Soc. 133 (2005), 13651369
MSC (2000):
Primary 34B15; Secondary 34B10
Published electronically:
October 18, 2004
MathSciNet review:
2111960
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: Shooting methods are employed to obtain solutions of the threepoint boundary value problem for the second order equation, where is continuous, and and conditions are imposed implying that solutions of such problems are unique, when they exist.
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 1.
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 2.
 M. Bohner and A.C. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, 2001. MR 1843232 (2002c:34002)
 3.
 C.J. Chyan, Uniqueness implies existence on time scales, J. Math. Anal. Appl. 258 (2001), 359365. MR 1828110 (2002e:34004)
 4.
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 5.
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 7.
 J. Henderson, Existence of solutions of right focal point boundary value problems for ordinary differential equations, Nonlin. Anal. 5 (1981), 9891002. MR 0633013 (82j:34015)
 8.
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 9.
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 12.
 L.K. Jackson and K. Schrader, Existence and uniqueness of solutions of boundary value problems for third order differential equations, J. Diff. Eqs. 9 (1971), 4654. MR 0269920 (42:4813)
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 A. Lasota and M. Luczynski, A note on the uniqueness of two point boundary value problems I, Zeszyty Naukowe UJ, Prace matematyezne 12 (1968), 2729. MR 0224900 (37:499)
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 G. Vidossich, On the continuous dependence of solutions of boundary value problems for ordinary differential equations, J. Diff. Eqs. 82 (1989), 114. MR 1023298 (90j:34036)
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 B. Yang, Boundary Value Problems for Ordinary Differential Equations, Ph.D. Dissertation, Mississippi State University, Mississippi State, MS, 2002.
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Additional Information
Johnny Henderson
Affiliation:
Department of Mathematics, Baylor University, Waco, Texas 767987328
Email:
Johnny_Henderson@baylor.edu
Basant Karna
Affiliation:
Department of Mathematics, Baylor University, Waco, Texas 767987328
Address at time of publication:
Department of Mathematics, Marshall University, Huntington, West Virginia 257552560
Email:
Basant_Karna@baylor.edu, karna@marshall.edu
Christopher C. Tisdell
Affiliation:
School of Mathematics, The University of New South Wales, Sydney 2052, Australia
Email:
cct@maths.unsw.edu.au
DOI:
http://dx.doi.org/10.1090/S0002993904076476
PII:
S 00029939(04)076476
Keywords:
Boundary value problem,
threepoint,
shooting method
Received by editor(s):
October 30, 2003
Received by editor(s) in revised form:
December 30, 2003
Published electronically:
October 18, 2004
Communicated by:
Carmen C. Chicone
Article copyright:
© Copyright 2004
American Mathematical Society
