Uniqueness of positive solutions for sturm-liouville boundary value problems

Proceedings of the American Mathematical Society

Volumn 126, Issue 2, 1998, Pages 365-374

  Wong, F U Hsiang ^a  

^a National Taipei Teacher's College   (Taiwan)

Author keywords

Positive solution; Singular and uniqueness; Sturm liouville BVPs

Indexed keywords

EID: 21944455180     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-98-04264-6     Document Type: Article

References (24)

1. R. P. Agarwal and V. Lakshmikantham, Uniqueness and nonuniqueness criteria for ordinary differential equations, World Scientific, Singapore, 1993. MR 96e:34002
2. L. E. Bobisud, Steady state turbulent flow with reaction, Rocky Mount. J. Math. 21 (1991), 993-1007. MR 93a:34026
3. H. Brezis and L. Oswald, Remarks on sublinear elliptic equations, Nonlinear Analysis T. M. & A. 19 (1986), 55-64. MR 87c:35057
4. R. Dalmasso, Uniqueness of positive and nonnegative solutions of nonlinear equations, Funkcial. Ekvac 37 (1994), 461-482. MR 97c:34037
5. _, Uniqueness of positive solutions of nonlinear second-order equations, Proc. Amer. Math. Soc. 123 (1995), 3417-3424. MR 96a:34035
6. D. De. Figueiredo, P. L. Lions and R. Nussbaum, A priori estimates and existence of positive solutions of semilinear elliptic equations, J. Math. Pures. App. 61 (1982), 41-63. MR 83h:35039
7. J. A. Gatica, V. Oliker and P. Waltman, Singular nonlinear boundary value problems for second-order ordinary differential equations, 79 (1989), 62-78. MR 90f:34030
8. B. Gidas, W. M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comrn. Math. Phys. 68 (1979), 209-243. MR 80h:35043
9. A. Granas, R. B. Guenther and J. W. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes (Rozprawy Mat) 244 (1985). MR 87a:34025
10. M. Guedda and L. Veron, Bifurcation phenomena associated to the p-Laplace operator, Trans. Amer. Math. Soc. 310 (1988), 419-431. MR 89j:35024
11. P. Hartman, Ordinary differential equations, Birkhauser, Boston, 1982. MR 83e:34002
12. H. G. Kaper, M. Knapp and M. K. Kwong, Existence theorems for second order boundary value problems, Differential Integral Equations 4 (1991), 543-554. MR 92m:34059
13. M. Krasnoselskii, Positive solutions of operator equations, Noordhoff, Groningen, 1964. MR 31:6107
14. M. K. Kwong, On the Kolodner-Coffman method for the uniqueness problem of Emden-Fowler BVP, Z. Angew. Math. Phys. 41 (1990), 79-104. MR 91b:34037
15. n, Arch. Rational. Mech. Anal. 105 (1989), 243-266. MR 90d:35015
16. P. L. Lions, On the existence of positive solutions of semilinear elliptic equations, SIAM Rev. 24 (1982), 441-467. MR 84a:35093
17. Y. Naito, Uniqueness of positive solutions of quasilinear differential equations, Differential Integral Equations 8 (1995), 1813-1822. MR 96g:34039
18. W. M. Ni and R. Nussbaum, Uniqueness and nonuniqueness for positive radial solutions of Δu + f(r, u) = 0, Comm. Pure. Appl. Math. 38 (1985), 69-108. MR 86d:35055
19. 2u′)′ + f(t,u) = 0, u(0) = u(T) = 0, p > 1, J. Differential Equations 80 (1989), 1-13. MR 91i:34018
20. M. del Pino and R. Manasevich, Multiple solutions for the p-Laplacian under global nonresonance, Proc. Amer. Math. Soc. 112 (1991), 131-138. MR 91h:34026
21. P. H. Rabinowitz, Minmax methods in critical point theory with applications to differential equations, CBMS Regional Conf. Ser. in Math., Amer. Math. Soc., Providence, RI, 1986. MR 87j:58024
22. Donal O'Regan, Theory of singular boundary value problems, World Scientific, Singapore, 1994. MR 95g:34003
23. F. H. Wong and S. L. Yu, Uniqueness of positive solutions for singular nonlinear boundary value problems, Hiroshima Mathematical Journal 26 (1996), 233-243. MR 97d:35044
24. F. H. Wong, Existence of positive solutions of singular boundary value problems, Nonlinear analysis T.M. & A. 21 (1993), 397-406. MR 941:34056