Multiple solutions for nonlinear operators and applications

Nonlinear Analysis, Theory, Methods and Applications

Volumn 66, Issue 9, 2007, Pages 1999-2015

  Sun, Jingxian ^a   Cui, Yujun ^b  

^a JIANGSU NORMAL UNIVERSITY   (China)

^b SHANDONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Cone; Multiple solutions theorem; O bounded cone; O positive operator; Topological degree

Indexed keywords

ABSTRACTING; MATHEMATICAL OPERATORS; ORDINARY DIFFERENTIAL EQUATIONS; THEOREM PROVING;

MULTIPLE SOLUTIONS THEOREM; O-BOUNDED CONE; O-POSITIVE OPERATOR; TOPOLOGICAL DEGREE;

NONLINEAR SYSTEMS;

EID: 33846903274     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.02.038     Document Type: Article

References (13)

1. Amann H. Fixed point equation and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18 (1976) 620-709
2. Amann H. Multiple positive fixed points of asymptotically linear maps. J. Funct. Anal. 17 (1974) 174-213
3. Dancer E.N., and Du Y. Existence of sign-changing solutions for some semilinear problems with jumping nonlinearities at zero. Proc. Roy. Soc. Edinburgh 124A (1994) 1165-1176
4. Guo D., Lakshmikantham V., and Liu X. Nonlinear Integral Equations in Abstract Spaces (1996), Kluwer Academic Publishers
5. Guo D., and Lakshmikantham V. Nonlinear Problems in Abstract Cones (1988), Academic press Inc., New York
6. Guo D., and Sun J. Nonlinear Integral Equations (1987), Shandong Science and Technology Press, Jinan (in Chinese)
7. Shivaji R. A remark on the existence of three solutions via sub-super solutions. Lect. Notes Pure and Appl. Math. 109 (1987) 561-566
8. Guo D. Nonlinear Functional Analysis[M]. second edn. (2001), Shandong Science and Technology Press, Jinan (in Chinese)
9. Deimling K. Nonlinear Functional Analysis[M] (1985), Springer-Verlag, New York
10. Sun J. Fixed point theorems of two-point extension type and applications. J. Systems Sci. Math. Sci. 12 2 (1992) 284-286 (in Chinese)
11. Zhang K., and Sun J. Existence of sign-changing solutions for nonlinear operator equations and its applications. Acta. Math. Sinica. 46 4 (2003) 815-822 (in Chinese)
12. Zhang K., and Sun J. The relation between sign-changing solution and positive-negative solutions for nonlinear operator equations and its applications. Acta. Math. Sci. 24B 3 (2004) 463-468 (in Chinese)
13. Del Pino M.A., and Manasevich R.F. Existence for a fourth-order boundary value problem under a two parameter nonresonance condition. Proc. Amer. Math. Soc. 112 (1991) 81-86