DOI QR코드

DOI QR Code

AN EXTENSION OF FIXED POINT THEOREMS CONCERNING CONE EXPANSION AND COMPRESSION AND ITS APPLICATION

  • Wang, Feng (SCHOOL OF MATHEMATICS AND PHYSICS JIANGSU POLYTECHNIC UNIVERSITY) ;
  • Zhang, Fang (SCHOOL OF MATHEMATICS AND PHYSICS JIANGSU POLYTECHNIC UNIVERSITY)
  • Published : 2009.04.30

Abstract

The famous Guo-Krasnosel'skii fixed point theorems concerning cone expansion and compression of norm type and order type are extended, respectively. As an application, the existence of multiple positive solutions for systems of Hammerstein type integral equations is considered.

References

  1. R. P. Agarwal, S. R. Grace, and D. ORegan, Semipositone higher-order differential equations, Appl. Math. Lett. 17 (2004), 201–207 https://doi.org/10.1016/S0893-9659(04)90033-X
  2. D. R. Anderson and R. I. Avery, Fixed point theorem of cone expansion and compression of functional type, J. Difference Equations Appl. 8 (2002), 1073–1083 https://doi.org/10.1080/10236190290015344
  3. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, New York, 1985
  4. P. Eloe and J. Henderson, Positive solutions for (n-1,1) conjugate boundary value problems, Nonlinear Anal. TMA 28 (1997), 1669–1680 https://doi.org/10.1016/0362-546X(95)00238-Q
  5. D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, San Diego, 1988
  6. D. Guo and J. Sun, Nonlinear Integral Equations, Shandong Press of Science and Technology, Jinan, 1987
  7. M. G. Krein and M. A. Rutman, Linear operators leaving invariant a cone in a Banach space, Transl. Amer. Math. Soc. 10 (1962), 199–325
  8. R. Ma and H. Wang, On the existence of positive solutions of fourth-order ordinary differential equations, Appl. Anal. 59 (1995), 225–231 https://doi.org/10.1080/00036819508840401
  9. R. Ma and H. Wang, Positive solutions of nonlinear three-point boundary-value problems, J. Math. Anal. Appl. 282 (2003), 232–240 https://doi.org/10.1016/S0022-247X(03)00141-0
  10. J. Sun and X. Liu, Computation for topological degree and its applications, J. Math. Anal. Appl. 202 (1996), 785–796 https://doi.org/10.1006/jmaa.1996.0347
  11. Z. Yang, Existence and nonexistence results for positive solutions of an integral boundary value problem, Nonlinear Anal. 65 (2006), 1489–1511 https://doi.org/10.1016/j.na.2005.10.025
  12. Z. Yang, Positive solutions of a second-order integral boundary value problem, J. Math. Anal. Appl. 321 (2006), 751–765 https://doi.org/10.1016/j.jmaa.2005.09.002
  13. Z. Yang, Nontrivial solutions of systems of nonlinear Hammerstein integral equations and applications, Mathematica Acta Scientia, 26A (2006), no. 2, 233–240
  14. Z. Yang and Donal O'Regan, Positive solvability of systems of nonlinear Hammerstein integral equations, J. Math. Anal. Appl. 311 (2005), 600–614 https://doi.org/10.1016/j.jmaa.2005.03.084
  15. Z. Yang and J. Sun, Positive solutions of boundary value problems for systems of nonlinear second order ordinary differential equations, Acta Mathematica Sinica, 47 (2004), 111–118
  16. E. Zeidler, Nonlinear Functional Analysis and its Applications I: Fixed-Point Theorems, Springer-Verlag, New York, 1986
  17. G. Zhang and J. Sun, A generalization of the cone expansion and compression fixed point theorem and applications, Nonlinear Anal. 67 (2007), 579–586 https://doi.org/10.1016/j.na.2006.06.003

Cited by

  1. Compression fixed point theorems of operator type vol.17, pp.1, 2015, https://doi.org/10.1007/s11784-015-0228-1