On the positive solutions of a nonlinear fourth-order boundary value problem with two parameters

International Journal of Phytoremediation

Volumn 83, Issue 1, 2004, Pages 97-107

  Yao, Qingliu ^a  

^a NANJING UNIVERSITY OF FINANCE AND ECONOMICS   (China)

Author keywords

Existence; Multiplicity; Nonexistence; Nonlinear fourth order boundary value problem; Positive solution

Indexed keywords

EID: 27344442755     PISSN: 15226514     EISSN: 15497879     Source Type: Journal    
DOI: 10.1080/00036810310001632817     Document Type: Article

References (16)

1. Gupta, CP. 1998. Existence and uniqueness results for the bending of an beam equation at resonance. J. Math. Anal. Appl., 135: 208–225.
2. Yang, Y. 1988. Fourth-order two-point boundary value problems. Appliable Analysis, 104: 175–180.
3. Gupta, CP. 1988. Existence and uniqueness theorems for the bending of an elastic beam equation. Applicable Analysis, 26: 289–304.
4. del Pino, MA, and Manasevich, RF. 1991. Existence for a fourth-order boundary value problem under a two-parameter nonresonance condition. Proc. Amer. Math. Soc., 112: 81–86.
5. Ma, R, and Wang, H. 1995. On the existence of positive solutions of fourth-order ordinary differential equations. Applicable Analysis, 59: 225–231.
6. Ma, R, Zhang, J, and Fu, S. 1997. The method of lower and upper solutions for fourth-order two-point boundary value problems. J. Math. Anal. Appl., 215: 415–422.
7. (4) (t) − λ h(t)f(u(t)) = 0 Chinese Annals of Math. 20A 575 578 (in Chinese)
8. Yao, Q. 2001. Several existence theorems for positive radial solutions to a semilinear elliptic BVP. Northeast. Math. J., 17: 169–174.
9. Yao, Q. 2001. The singular second-order nonlinear eigenvalue problem with infinitely many positive solutions. Annals of Diff. Eqns., 17: 268–274.
10. Yao Q, 2001 Existence and multiplicity of positive radial solutions for a class of nonlinear elliptic equations in annular domains Chinese Annals of Math. 22A 633 638 (in Chinese)
11. Yao, Q, and Ma, Q. 2002. Existence of positive radial solutions for some semilinear elliptic equations in annulus. Applied Math. & Mech., 23: 1452–1457.
12. Yao, Q. 2002. The positive solution of classical Gelfand model with coefficient that change sign. Applied Math. & Mech., 23: 1458–1463.
13. Yao, Q. 2003. Existence and multiplicity of positive radial solutions for a semilinear elliptic equation with change of sign. Applicable Analysis, 80: 65–77.
14. Yao, Q. 2003. On the positive solutions of Lidstone boundary value problems. Applied Math. & Comput., 137: 477–485.
15. Zauderer E, 1983 Partial Differential Equations of Applied Mathematics, Wiley Interscience New York
16. Krasnosel'skii MA, 1964 Positive Solutions of Operator Equations, Noordhoff Groningen Netherland