Multiple positive solutions of resonant and non-resonant nonlocal boundary value problems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 71, Issue 3-4, 2009, Pages 1369-1378

  Webb, J R L ^a   Zima, M ^b  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b UNIVERSITY OF RZESZÓW   (Poland)

Author keywords

Fixed point index; Nonlocal boundary conditions; Positive solution; Resonance

Indexed keywords

AT RESONANCES; FIXED POINT INDEX; MULTIPLE POSITIVE SOLUTIONS; NON-RESONANT; NONLOCAL BOUNDARY CONDITIONS; NONLOCAL BOUNDARY-VALUE PROBLEMS; PERTURBED EQUATIONS; PERTURBED PROBLEMS; POSITIVE SOLUTION;

ORDINARY DIFFERENTIAL EQUATIONS; RESONANCE;

BOUNDARY CONDITIONS;

EID: 67349103328     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2008.12.010     Document Type: Article

References (21)

1. Feng W., and Webb J.R.L. Solvability of m-point boundary value problems with nonlinear growth. J. Math. Anal. Appl. 212 (1997) 467-480
2. Gupta C.P. Existence theorems for a second order m-point boundary value problem at resonance. Internat. J. Math. Math. Sci. 18 (1995) 705-710
3. Infante G., and Zima M. Positive solutions of multi-point boundary value problems at resonance. Nonlinear Anal. TMA 69 (2008) 2458-2465
4. Ma R. Existence results of a m-point boundary value problem at resonance. J. Math. Anal. Appl. 294 (2004) 147-157
5. Zhang G., and Sun J. Positive solutions of m-point boundary value problems. J. Math. Anal. Appl. 291 (2004) 406-418
6. Han X. Positive solutions for a three-point boundary value problems at resonance. J. Math. Anal. Appl. 336 (2007) 556-568
7. Han X. Positive solutions for a three-point boundary value problem. Nonlinear Anal. TMA 66 (2007) 679-688
8. Bai C., and Fang J. Existence of positive solutions for three-point boundary value problems at resonance. J. Math. Anal. Appl. 291 (2004) 538-549
9. Bai Z., Li W., and Ge W. Existence and multiplicity of solutions for four-point boundary value problems at resonance. Nonlinear Anal. TMA 60 (2005) 1151-1162
10. Kosmatov N. A symmetric solution of a multipoint boundary value problem at resonance. Abstr. Appl. Anal. (2006) 11 Art. ID 54121
11. Kosmatov N. Multi-point boundary value problems on an unbounded domain at resonance. Nonlinear Anal. TMA 68 (2008) 2158-2171
12. Liu B. Solvability of multi-point boundary value problem at resonance. IV. Appl. Math. Comput. 143 (2003) 275-299
13. Liu B., and Zhao Z. A note on multi-point boundary value problems. Nonlinear Anal. TMA 67 (2007) 2680-2689
14. Mawhin J. Equivalence theorems for nonlinear operator equations and coincidence degree theory for mappings in locally convex topological vector spaces. J. Differential Equations 12 (1972) 610-636
15. O'Regan D., and Zima M. Leggett-Williams norm-type theorems for coincidences. Arch. Math. 87 (2006) 233-244
16. Ma R., and Yang Y. Existence result for a singular nonlinear boundary value problem at resonance. Nonlinear Anal. TMA 68 (2008) 671-680
17. Webb J.R.L., and Infante G. Positive solutions of nonlocal boundary value problems involving integral conditions. NoDEA Nonlinear Differential Equations Appl. 15 (2008) 45-67
18. Webb J.R.L., and Infante G. Positive solutions of nonlocal boundary value problems: A unified approach. J. London Math. Soc. (2) 74 (2006) 673-693
19. Krasnosel'skiǐ M.A., and Zabreǐko P.P. Geometrical Methods of Nonlinear Analysis (1984), Springer-Verlag, Berlin
20. Webb J.R.L., and Lan K.Q. Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type. Topol. Methods Nonlinear Anal. 27 (2006) 91-116
21. Nussbaum R.D. Periodic solutions of some nonlinear integral equations. Dynamical Systems (Proc. Internat. Sympos., Univ. Florida, Gainesville, Fla., 1976) (1977), Academic Press, New York 221-249