Existence of solutions for three-point boundary value problems for second order equations

Proceedings of the American Mathematical Society

Volumn 133, Issue 5, 2005, Pages 1365-1369

  Henderson, Johnny ^a   Karna, Basant ^a,b   Tisdell, Christopher C ^c  

^a BAYLOR UNIVERSITY   (United States)

^b MARSHALL UNIVERSITY   (United States)

^c UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Boundary value problem; Shooting method; Three point

Indexed keywords

EID: 18144365855     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-04-07647-6     Document Type: Article

References (20)

1. C. Bai and J. Fang, Existence of multiple positive solutions for nonlinear m-point boundary value problems, J. Math. Anal. Appl. 281 (2003), 76-85. MR1980075 (2004b:34035)
2. M. Bonner and A.C. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, 2001. MR1843232 (2002c:34002)
3. C.J. Chyan, Uniqueness implies existence on time scales, J. Math. Anal. Appl. 258 (2001), 359-365. MR1828110 (2002e:34004)
4. J.M. Davis and J. Henderson, Uniqueness implies existence for fourth-order Lidstone boundary value problems, Panamer. Math. J. 8 (1998), 23-35. MR1657450 (99i:34033)
5. C.P. Gupta and S.I. Trofimchuk, Solvability of a multi-point boundary value problem and related a priori estimates, Canad. Appl. Math. Quart. 6 (1998), 45-60. MR1638415 (99f:34020)
6. P. Hartman, On N-parameter families and interpolation problems for nonlinear ordinary differential equations, Trans. Amer. Math. Soc. 154 (1971), 201-226. MR0301277 (46:435)
7. J. Henderson, Existence of solutions of right focal point boundary value problems for ordinary differential equations, Nonlin. Anal. 5 (1981), 989-1002. MR0633013 (82j:34015)
8. J. Henderson, Existence theorems for boundary value problems for nth-order nonlinear difference equations, SIAM J. Math. Anal. 20 (1989), 468-478. MR0982673 (90a:39003)
9. J. Henderson, Focal boundary value problems for nonlinear difference equations, I, II, J. Math. Anal. Appl. 141 (1989), 559-567, 568-579. MR1009063 (90g:39003)
10. J. Henderson and W.K.C. Yin, Existence of solutions for fourth order boundary value problems on a time scale, J. Differ. Eqs. Appl. 9 (2003), 15-28. MR1958300 (2003k:34041)
11. J. Henderson and W.K.C. Yin, Two-point and three-point problems for fourth order dynamic equations, Dynam. Systems Appl. 12 (2003), 159-169. MR1989029 (2004d:34034)
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), 46-54. MR0269920 (42:4813)
13. G. Klaasen, Existence theorems for boundary value problems of nth order ordinary differential equations, Rocky Mtn. J. Math. 3 (1973), 457-472. MR0357944 (50:10409)
14. A. Lasota and M. Luczynski, A note on the uniqueness of two point boundary value problems I, Zeszyty Naukowe UJ, Prace matematyezne 12 (1968), 27-29. MR0224900 (37:499)
15. Ruyun Ma, Existence theorems for a second-order three-point boundary value problem, J. Math. Anal. Appl. 212 (1997), 430-442. MR1464888 (98h:34041)
16. Ruyun Ma, Existence and uniqueness of solutions to first-order three-point boundary value problems, Appl. Math. Lett. 15 (2002), 211-216. MR1880760 (2002k:34032)
17. A.C. Peterson, Existence-uniqueness for focal-point boundary value problems, SIAM J. Math. Anal. 12 (1981), 173-185. MR0605428 (83h:34017)
18. E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966. MR0210112 (35:1007)
19. G. Vidossich, On the continuous dependence of solutions of boundary value problems for ordinary differential equations, J. Diff. Eqs. 82 (1989), 1-14. MR1023298 (90j:34036)
20. B. Yang, Boundary Value Problems for Ordinary Differential Equations, Ph.D. Dissertation, Mississippi State University, Mississippi State, MS, 2002.