Global behavior of positive solutions of nonlinear three-point boundary value problems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 60, Issue 4, 2005, Pages 685-701

  Ma, Ruyun ^a,b   Thompson, Bevan ^b  

^a NORTHWEST NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Bifurcation; Continuum; Global continuation principle of Leray Schauder; Multi point boundary value problems; Positive solutions

Indexed keywords

BOUNDARY VALUE PROBLEMS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

BIFURCATIONS; CONTINUUM; GLOBAL CONTINUATION PRINCIPLE OF LERAY-SCHAUDER; MULTI-POINT BOUNDARY VALUE PROBLEMS; POSITIVE SOLUTIONS;

NONLINEAR EQUATIONS;

EID: 10644269829     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.09.044     Document Type: Article

References (18)

1. H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM. Rev. 18 (1976) 620-709.
2. A. Ambrosetti, P. Hess, Positive solutions of asymptotically linear elliptic eigenvalue problems, J. Math. Anal. Appl. (73) (2) (1980) 411-422.
3. M.S. Berger, L.F. Fraenkel, Nonlinear desingularization in certain free-boundary problems, Commun. Math. Phys. 77 (2) (1980) 149-172.
4. L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (2) (1991) 494-505.
5. L. Byszewski, Application of properties of the right-hand sides of evolution equations to an investigation of nonlocal evolution problems, Nonlinear Anal. 33 (5) (1998) 413-426.
6. L. Byszewski, Abstract nonlinear nonlocal problems and their physical interpretation, in: H. Akca, V. Covachev, E. Litsyn (Eds.), Biomathematics, Bioinformatics and Applications of Functional Differential Equations, Akdeniz Univ. Publ., Antalya, Turkey, 1999.
7. L.H. Erbe, H.Y. Wang, On the existence of positive solutions of ordinary value problems, Proc. Amer. Math. Soc. 120 (3) (1994) 743-748.
8. C.P. Gupta, A sharper condition for solvability of a three-point boundary value problem, J. Math. Anal. Appl. 205 (1997) 586-597.
9. D. Jackson, Existence and uniqueness of solutions to semilinear nonlocal parabolic equations, J. Math. Anal. Appl. 172 (1) (1993) 256-265.
10. K.Q. Lan, J.R.L. Webb, Positive solutions of semilinear differential equations with singularities, J. Differential Equations 148 (1998) 407-421.
11. R.Y. Ma, Positive solutions of a nonlinear three-point boundary value problem, Electron. J. Differential Equations 1999 (34) (1999) 1-8.
12. C.V. Pao, Reaction diffusion equations with nonlocal boundary and nonlocal initial conditions, J. Math. Anal. Appl. 195 (3) (1995) 702-718.
13. P.H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal. 7 (1971) 487-513.
14. B. Ruf, Remarks and generalizations related to a recent multiplicity result of A. Lazer and P. McKenna, Nonlinear Anal. TMA 9 (12) (1985) 1325-1330.
15. B.P. Rynne, Global bifurcation for 2mth-order boundary value problems and infinity many solutions of superlinear problems, J. Differential Equations 188 (2003) 461-472.
16. S.P. Timoshenko, Theory of Elastic Stability, McGraw-Hill, New York, 1961.
17. J.R. Webb, Positive solutions of some three-point boundary value problems via fixed point index theory, Nonlinear Anal. 47 (2001) 4319-4332.
18. E. Zeidler, Nonlinear Functional Analysis, I: Fixed-Point Theorems, Springer, Berlin, 1993.