Existence of Multiple Solutions for Second Order Boundary Value Problems

Journal of Differential Equations

Volumn 166, Issue 2, 2000, Pages 443-454

  Henderson, Johnny ^a   Thompson, H B ^b  

^a AUBURN UNIVERSITY   (United States)

^b UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Bernstein Nagumo growth condition; Lower solutions; Multiple solutions; Schauder degree; Two point boundary value problems; Upper solutions

Indexed keywords

EID: 0034692193     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3797     Document Type: Article

References (14)

1. Ako K. Subfunctions for ordinary differential equations II. Funckial. Ekvac. 10:1967;145-162.
2. Ako K. Subfunctions for ordinary differential equations III. Funckial. Ekvac. 11:1968;111-129.
3. Avery R. I., Peterson A. C. Multiple positive solutions of a discrete second order conjugate problem. PanAmer. Math. J. 8:1998;1-12.
4. Anderson D. Multiple positive solutions for a three-point boundary value problem. Math. Comput. Modelling. 27:1998;49-57.
5. Avery R. Existence of multiple positive solutions to a conjugate boundary value problem. MSR Hot-Line. 2:1998.
6. Jackson L. K. Subfunctions and second-order ordinary differential inequalities. Adv. in Math. 2:1968;307-363.
7. Deimling K. Nonlinear Functional Analysis. 1985;Springer-Verlag, New York.
8. Guo D., Lakshmikantham V. Nonlinear Problems in Abstract Cones. 1988;Academic Press, San Diego.
9. Henderson J., Thompson H. B. Existence of multiple solutions for some n th order boundary value problems. Comm. Appl. Nonlinear Anal. 7:2000;57-62.
10. Leggett R. W., Williams L. R. Multiple positive fixed points of nonlinear operators on ordered Banach spaces. Indiana Univ. Math. 28:1979;673-688.
11. Yong S., Jingxian S. Multiple positive fixed points of weakly inward mappings. J. Math. Anal. Appl. 148:1990;431-439.
12. Thompson H. B. Existence of solutions for a two point boundary value problem. Rend. Circ. Mat. Palermo (2). XXXV:1986;261-275.
13. Thompson H. B. Minimal solutions for two point boundary value problems. Rend. Circ. Mat. Palermo (2). XXXVII:1988;261-281.
14. Thompson H. B. Second order ordinary differential equations with fully nonlinear two point boundary conditions. Pacific J. Math. 172:1996;255-277.