Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

POSITIVE SOLUTIONS TO A FOUR-POINT BOUNDARY VALUE PROBLEM OF HIGHER-ORDER DIFFERENTIAL EQUATION WITH A P-LAPLACIAN

  • Pang, Huihui (College of Science, China Agricultural University) ;
  • Lian, Hairong (School of Information Engineering, China University of Geosciences) ;
  • Ge, Weigao (Department of Mathematics, Beijing Institute of Technology)
  • Published : 2010.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we obtain the existence of positive solutions for a quasi-linear four-point boundary value problem of higher-order differential equation. By using the fixed point index theorem and imposing some conditions on f, the existence of positive solutions to a higher-order four-point boundary value problem with a p-Laplacian is obtained.

Keywords

References

  1. V.A. Il'in, E.I. Moiseev, Nonlocal boundary value problem of second kind for a Sturm Liouville operator, Differential Equation, 23 (1987), 979-987.
  2. W. Feng, On an m-point boundary value problem, Nonlinear Anal., 30 (1997) , 5369-5374. https://doi.org/10.1016/S0362-546X(97)00360-X
  3. W. Feng, J.R. L. Webb, Solvability of m-point boundary value problem with nonlineargrowth, J. Math. Anal. Appl., 212 (1997), 467-480. https://doi.org/10.1006/jmaa.1997.5520
  4. C.P. Gupta, A generalized multi-point boundary value problem for second order ordinary differential equation, Appl. Math. Comput., 89 (1998), 133-146. https://doi.org/10.1016/S0096-3003(97)81653-0
  5. R.Ma, Existence of solutions of nonlinear m-point boundary value problems, J. Math. Anal. Appl., 256 (2001), 556-567. https://doi.org/10.1006/jmaa.2000.7320
  6. D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cone, Academic Press, San Diego,1988.
  7. D. Guo, V. Lakshmikantham, X. Liu, Nonlinear Intergral Equations in Abstract Spaces, Kluwer Academic, Dordrecht.
  8. H. Su et al., Positive solutions of four-point boundary value problems for higher-order p-Laplacian operator, J. Math. Anal. Appl., 330 (2007), 836-851. https://doi.org/10.1016/j.jmaa.2006.07.017
  9. P.J.Y. Wong, R. P. Agarwal, On eigenvalue intervals and twin eigenfunctions of higherorder boundary value problems, Comp. Appl. Math., 88 (1998), 15-43. https://doi.org/10.1016/S0377-0427(97)00202-1