Existence result for a singular nonlinear boundary value problem at resonance

Nonlinear Analysis, Theory, Methods and Applications

Volumn 68, Issue 3, 2008, Pages 671-680

  Ma, Ruyun ^a   Yang, Yunrui ^a  

^a NORTHWEST NORMAL UNIVERSITY   (China)

Author keywords

Connectivity; Lyapunov Schmidt procedure; Resonance; Solution set

Indexed keywords

LYAPUNOV METHODS; PROBLEM SOLVING; RESONANCE;

CONNECTIVITY; LYAPUNOV SCHMIDT PROCEDURES;

BOUNDARY VALUE PROBLEMS;

EID: 36148992916     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.11.030     Document Type: Article

References (18)

1. Agarwal R., and O'Regan D. Singular Differential and Integral Equations with Applications (2003), Kluwer Academic Publishers, London
2. Agarwal R., and O'Regan D. Some new results for singular problems with sign changing nonlinearities. Fixed point theory with applications in nonlinear analysis. J. Comput. Appl. Math. 113 1-2 (2000) 1-15
3. Ahmad S. Multiple nontrivial solutions of resonant and non-resonant asymptotically linear problems. Proc. Amer. Math. Soc. 96 3 (1986) 405-409
4. Ambrosetti A., and Mancini G. Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance. The case of the simple eigenvalue. J. Differential Equations 28 2 (1978) 220-245
5. Asakawa H. Nonresonant singular two-point boundary value problems. Nonlinear Anal., TMA 44 6 (2001) 791-809
6. Bobisud L.E., and O'Regan D. Positive solutions for a class of nonlinear singular boundary value problems at resonance. J. Math. Anal. Appl. 184 2 (1994) 263-284
7. Costa D.G., and Gonçalves J.V.A. Existence and multiplicity results for a class of nonlinear elliptic boundary value problems at resonance. J. Math. Anal. Appl. 84 2 (1981) 328-337
8. Gupta C.P. Solvability of a boundary value problem with the nonlinearity satisfying a sign condition. J. Math. Anal. Appl. 129 2 (1988) 482-492
9. Habets P., and Zanolin F. Upper and lower solutions for a generalized Emden-Fowler equation. J. Math. Anal. Appl. 181 3 (1994) 684-700
10. Habets P., and Zanolin F. Positive solutions for a class of singular boundary value problems. Boll. Un. Mat. Ital. 9 2 (1995) 273-286
11. Natanson I.P. Theory of Functions of a Real Variable vol. 2 (1955), Ungar, New York Translated Russian into Chinese by Xu Ruiyun
12. Landesman E.M., and Lazer A.C. Nonlinear perturbations of linear elliptic boundary value problems at resonance. J. Math. Mech. 19 (1969/1970) 609-623
13. Iannacci R., and Nkashama M.N. Unbounded perturbations of forced second order ordinary differential equations at resonance. J. Differential Equations 69 3 (1987) 289-309
14. Iannacci R., and Nkashama M.N. Nonlinear two-point boundary value problems at resonance without Landesman-Lazer condition. Proc. Amer. Math. Soc. 106 4 (1989) 943-952
15. Ma R. Multiplicity results for a third order boundary value problem at resonance. Nonlinear Anal. 32 4 (1998) 493-499
16. Mawhin J. Topological degree methods in nonlinear boundary value problems. CBMS Regional Conference Series in Mathematics vol. 40 (1979), American Mathematical Society, Providence, RI
17. O'Regan D. Singular Dirichlet boundary value problems. II. Resonance case. Czechoslovak Math. J. 48 123 (1998) 269-290
18. Taliaferro S.D. A nonlinear singular boundary value problem. Nonlinear Anal. 3 6 (1979) 897-904