Generalization for Amann's and Leggett-Williams' three-solution theorems and applications

Journal of Mathematical Analysis and Applications

Volumn 298, Issue 2, 2004, Pages 638-654

  Li, Fuyi ^a   Han, Guodong ^a  

^a SHANXI UNIVERSITY   (China)

Author keywords

Completely continuous operator; Cone; Fixed point index; Retract; Three solution theorem

Indexed keywords

EID: 10144237214     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.06.001     Document Type: Article

References (16)

1. Amann H. On the number of solutions of nonlinear equations in ordered Banach spaces J. Funct. Anal. 11 1972 346-384
2. Amann H. Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces SIAM Rev. 18 1976 620-709
3. Avery R.I. A generalization of the Leggett-Williams fixed point theorem Math. Sci. Res. Hot-Line 3 1999 9-14
4. Davis J.M. Eloe P.W. Henderson J. Triple positive solutions and dependence on higher order derivatives J. Math. Anal. Appl. 237 1999 710-720
5. Davis J.M. Henderson J. Wong P.J.Y. General Lidstone problems: Multiplicity and symmetry of solutions J. Math. Anal. Appl. 251 2000 527-548
6. Deimling K. Nonlinear Functional Analysis 1985 Springer-Verlag Berlin
7. Erbe L.H. Hu S. Wang H. Multiple positive solutions of some boundary value problems J. Math. Anal. Appl. 184 1994 640-648
8. Graef J.R. Qian C. Yang B. Multiple symmetric positive solutions of a class of boundary value problem for higher order ordinary differential equations Proc. Amer. Math. Soc. 131 2002 577-585
9. Guo D. Nonlinear Functional Analysis 1985 Shandong Science and Technology (in Chinese)
10. Guo D. Lakshmikantham V. Nonlinear Problems in Abstract Cones 1988 Academic Press London
11. Henderson J. Thompson H.B. Multiple symmetric positive solutions for a second order boundary problem Proc. Amer. Math. Soc. 128 2000 2373-2379
12. Leggett R.W. Williams L.R. Multiple positive fixed points of nonlinear operators on ordered Banach spaces Indiana Univ. Math. J. 28 1979 673-688
13. Li F. Improvement on Amann's three solution theorem and applications J. Systems Sci. Math. Sci. 19 1999 403-406 (in Chinese)
14. Li F. Liu Z. Multiple solutions of some nonlinear operator equations and applications Acta Math. Sinica 41 1998 97-102 (in Chinese)
15. Li F. Zhang Y. Multiple symmetric nonnegative solutions of second-order ordinary differential equations Appl. Math. Lett. 17 2004 261-267
16. Liu Z. Li F. Multiple positive solutions of nonlinear two-point boundary value problems J. Math. Anal. Appl. 203 1996 610-625