Higher order non-local (n-1,1) conjugate type boundary value problems

AIP Conference Proceedings

Volumn 1124, Issue , 2009, Pages 332-341

  Webb, J R L ^a  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

Conjugate type boundary conditions; Higher order equations; Nonlocal boundary conditions

Indexed keywords

EID: 67650547495     PISSN: 0094243X     EISSN: 15517616     Source Type: Conference Proceeding    
DOI: 10.1063/1.3142949     Document Type: Conference Paper

References (20)

1. R. P. Agarwal and D. O'Regan, Midtiplicity results for singidar conjugate, focal, and N,P problems, J. Differential Equations 170 (2001), 142-156.
2. P. W. Eloe and J. Henderson, Positive solutions for (n - 1,1) conjugate boundary value problems, Nonlinear Anal. 28 (1997), 1669-1680.
3. P. W. Eloe and B. Ahmad, Positive solutions of a nonlinear n-th order boundary value problem with nonlocal conditions, Appl. Math. Lett. 18, (2005), 521-527.
4. D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, 1988.
5. Y. Guo, Y. Ji, and J. Zhang, Three positive solutions for a nonlinear nth-order m-point boundary value problem. Nonlinear Anal. 68 (2008) 3485-3492.
6. X. Hao, L. Liu, and Y Wu, Positive solutions for nonlinear nth-order singidar nonlocal boundary value problems. Bound. Value Probl. (2007), Art. ID 74517, 10 pp.
7. Weihua Jiang, Midtiple positive solutions for nth-order m-point boundary value problems with all derivatives, Nonlinear Anal., 68, 1064-1072.
8. L. Kong and J. Wang, The Green's function for k,n - k conjugate boundary value problems and its applications, J. Math. Anal. Appl., 255 (2001), 404-422.
9. M. A. Krasnosel'skiǐ and P. P. Zabreǐko, Geometrical methods of nonlinear analysis, Springer-Verlag, Berlin, 1984.
10. K. Q. Lan and J. R. L. Webb, Positive solutions of semilinear differential equations with singidarities, J. Differential Equations, 148, (1998), 407-421.
11. K. Q. Lan, Multiple positive solutions of conjugate boundary value problems with singiularities, Applied Math. Comput., 147 (2004), 461-474.
12. R. D. Nussbaum, Eigenvectors of order preserving linear operators, J. London Math. Soc. (2), 58 (1996), 480-496.
13. C. Pang, W. Dong, and Z. Wei, Green's function and positive solutions of nth order m-point boundary value problem, Appl. Math. Comput., 182 (2006), 1231-1239.
14. Y. Sun, Y. J. Cho,D. O'Regan, On the existence of positive solutions for singular third order boundary value problems. Int. J. Evol. Equ., 1 (2005), 403-413.
15. J. R. L. Webb and K. Q. Lan, Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type, Topol. Methods Nonlinear Anal., 27 (2006), 91-116.
16. J. R. L. Webb and G. Infante, Positive solutions of nonlocal boundary value problems involving integral conditions, NoDEA Nonlinear Differential Equations Appl., 15 (2008), 45-67.
17. J. R. L. Webb and G. Infante, Positive solutions of nonlocal boundary value problems: a unified approach, J. London Math. Soc. (2), 74 (2006), 673-693.
18. J. R. L. Webb, G. Infante and D. Franco, Positive solutions of nonlinear fourth order boundary value problems with local and nonlocal boundary conditions, Proc. Roy. Soc. Edinburgh, 138A (2008), 427-446.
19. J. R. L. Webb and G. Infante, Nonlocal boundary value problems of arbitrary order, J. London Math. Soc.(2) 79 (2009), 238-258.
20. J. R. L. Webb, Non-local conjugate type boundary value problems of higher order. Nonlinear Anal., in press.