Positive solutions for a higher-order four-point boundary value problem with a p-Laplacian

Computers and Mathematics with Applications

Volumn 58, Issue 6, 2009, Pages 1103-1112

  Zhao, Junfang ^a   Ge, Weigao ^a  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Cone; Fixed point theorem; Higher order; Multi point boundary value problem; Positive solution

Indexed keywords

FIXED POINT THEOREM; FIXED POINT THEOREM IN CONES; FOUR-POINT BOUNDARY VALUE PROBLEM; HIGHER ORDER; MULTI-POINT BOUNDARY VALUE PROBLEM; MULTIPLE POSITIVE SOLUTIONS; P-LAPLACIAN; POSITIVE SOLUTION;

BOUNDARY VALUE PROBLEMS; LAPLACE TRANSFORMS;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 68849116996     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.04.022     Document Type: Article

References (33)

1. Aronson D., Crandall M.G., and Peletier L.A. Stabilization of solutions of a degenerate nonlinear diffusion problem. Nonlinear Anal. 6 (1982) 1001-1022
2. Bandle C., and Kwong M.K. Semilinear elliptic problems in annular domains. J. Appl. Math. Phys. 40 (1989) 245-257
3. Choi Y.S., and Ludford G.S. An unexpected stability result of the near-extinction diffusion flame for non-unity Lewis numbers. Q. J. Mech. Appl. Math. 42 Part 1 (1989) 143-158
4. Cohen D.S. Multiple stable solutions of nonlinear boundary value problems arising in chemical reactor theory. SIAM J. Appl. Math. 20 (1971) 1-13
5. Dancer E.N. On the structure of solutions of an equation in catalysis theory when a parameter is large. J. Differential Equations 37 (1980) 404-437
6. Dang H., and Schmitt K. Existence of positive solutions for semilinear elliptic equations in annular domain. J. Differential Integral Equs. 7 (1994) 747-758
7. Dulcska E. Soil settlement effects on buildings. Developments in Geotechnical Engineering vol. 69 (1992), Elsevier, Amsterdam
8. Garaizar X. Existence of positive radial solutions for semilinear elliptic equations in the annulus. J. Differential Equations 70 (1987) 69-72
9. Iffland G. Positive solutions of a problem of Emden-Fowler type with a free boundary. SIAM J. Math. Anal. 18 (1987) 283-292
10. Santanilla J. Nonnegative solutions to boundary value problems for nonlinear first and second order ordinary differential equations. J. Math. Anal. Appl. 126 (1987) 397-408
11. Timoshenko S.P. Theory of Elastic Stability (1961), McGraw-Hill, New York
12. Wang H. On the existence of positive solutions for semilinear elliptic equations in the annulus. J. Differential Equations 109 (1994) 1-7
13. Soedel W. Vibrations of Shells and Plates (1993), Dekker, New York
14. Agarwal R.P., and Wong F.H. Existence of positive solutions for non-positive higher-order BVPs. J. Comput. Appl. Math. 88 (1998) 3-14
15. Agarwal R.P. Focal Boundary Value Problems for Differential and Difference Equations (1998), Kluwer Academic, Dordrecht
16. Agarwal R.P., O'Regan O., and Wong P.J.Y. Positive Solutions of Differential, Difference, and Integral Equations (1998), Kluwer Academic, Dordrecht
17. Agarwal R.P., and Wong F.H. Existence of positive solutions for higher order difference equations. Appl. Math. Lett. 10 (1997) 67-74
18. Anderson D.R., and Davis J.M. Multiple solutions and eigenvalues for third-order right focal boundary value problem. J. Math. Anal. Appl. 267 (2002) 135-157
19. Chyan C.J., and Henderson J. Positive solutions for singular higher order nonlinear equations. Differential Equations Dynam. Systems 2 (1994) 153-160
20. Graef J.R., and Yang B. On a nonlinear boundary value problem for fourth order equations. Appl. Anal. 72 (1999) 439-448
21. Hao Z., and Liu L. A necessary and sufficiently condition for the existence of positive solution of fourth-order singular boundary value problems. Appl. Math. Lett. 16 (2003) 279-285
22. Moshinsky M. Sobre los problemas de condiciones a la frontiera en una dimension de caracteristicas discontinuas. Bol. Soc. Mat. Mexicana 7 (1950) 10-25
23. Timoshenko S. Theory of Elastic Stability (1961), McGraw-Hill, New York
24. Zou Y., Hu Q., and Zhang R. On numerical studies of multi-point boundary value problem and its fold bifurcation. Appl. Math. Comput. 185 (2007) 527-537
25. Il'in V.A., and Moiseev E.I. Nonlocal boundary value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects. Differential Equations 23 (1987) 803-810
26. W Z., and P Ch. Positive solutions and multiplicity of fourth-order m-point boundary value problems with two parameters. Nonlinear Anal. 67 (2007) 1586-1598
27. Feng W., and Webb J.R.L. Solvability of m-point boundary value problems with nonlinear growth. J. Math. Anal. Appl. 212 (1997) 467-480
28. Ma R. Positive solutions of a nonlinear three-point boundary value problem. Electron. J. Differential Equations 34 (1999) 1-8
29. Su H., Wang B., Wei Z., and Zhang X. Positive solutions of four-point boundary value problems for higher-order p-Laplacian operator. J. Math. Anal. Appl. 330 (2007) 836-851
30. Sun B., and Ge W. Existence and iteration of positive solutions to a class of Sturm-Liouville-like p-Laplacian boundary value problems. Nonlinear Anal. 69 (2008) 1454-1461
31. Liu B. Positive solutions of three-point boundary value problems for the one-dimensional p-Laplacian with infinitely many singularities. Appl. Math. Lett. 17 (2004) 655-661
32. Lian H., and Ge W. Positive solutions for a four-point boundary value problem with the p-Laplacian. Nonlinear Anal. 68 (2008) 3493-3503
33. Guo D., and Lakshmikantham V. Nonlinear Problems in Abstract Cones (1988), Academic Press, San Diego, CA