Existence and nonexistence of positive solutions for a class of nth-order three-point boundary value problems in Banach spaces

Nonlinear Analysis, Theory, Methods and Applications

Volumn 70, Issue 2, 2009, Pages 584-597

  Zhang, Xuemei ^a,c   Feng, Meiqiang ^b,c   Ge, Weigao ^c  

^a NORTH CHINA ELECTRIC POWER UNIVERSITY   (China)

^b BEIJING INFORMATION TECHNOLOGY INSTITUTE   (China)

^c BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Existence; Fixed point index theory; Measure of noncompactness; Multi point boundary value problem; Positive solution

Indexed keywords

BANACH SPACES; BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; INITIAL VALUE PROBLEMS; NONLINEAR EQUATIONS; OPTIMAL CONTROL SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; SOLUTIONS; TOPOLOGY; TURBULENT FLOW;

EXISTENCE; FIXED-POINT INDEX THEORY; MEASURE OF NONCOMPACTNESS; MULTI-POINT BOUNDARY VALUE PROBLEM; POSITIVE SOLUTION;

PROBLEM SOLVING;

EID: 56049110598     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.12.028     Document Type: Article

References (31)

1. Gupta C.P. A generalized multi-point boundary value problem for second order ordinary differential equations. Appl. Math. Comput. 89 (1998) 133-146
2. Gupta C.P., Ntouyas S.K., and Tsamatos P.Ch. Solvability of an m-point boundary value problem for second order ordinary differential equations. J. Math. Anal. Appl. 189 (1995) 575-584
3. Chen S., Hu J., Chen L., and Wang C. Existence results for n-point boundary value problem of second ordinary differential equations. J. Comput. Appl. Math. 180 (2005) 425-432
4. Zhang Z., and Wang J. The upper and lower solution method for a class of singular nonlinear second order three-point boundary value problems. J. Comput. Appl. Math. 147 (2002) 41-52
5. Agarwal R.P., and O'Regan D. Right focal singular boundary value problems. Z. Angew. Math. Mech. 79 (1999) 363-373
6. Agarwal R.P., and O'Regan D. Multiplicity results for singular conjugate, focal, and (n, p) problems. J. Differential Equations 170 (2001) 142-156
7. Agarwal R.P. Focal boundary value problems for differential and difference equations (1998), Kluwer, Dordrecht
8. Agarwal R.P., O'Regan D., and Wong P.J.Y. Positive solutions of differential, difference and integral equations (1999), Kluwer Academic, Dordrecht
9. Eloe P.W., and Ahmad B. Positive solutions of a nonlinear nth order boundary value problem with nonlocal conditions. Appl. Math. Lett. 18 (2005) 521-527
10. Graef J.R., Henderson J., and Yang B. Positive solutions of a nonlinear higher order boundary-value problem. Electron. J. Differential Equations 2007 45 (2007) 1-10
11. Guo D.J., and Lakshmikantham V. Multiple solutions of two-point boundary value problems of ordinary differential equations in Banach spaces. J. Math. Anal. Appl. 129 (1988) 211-222
12. Guo D.J., Lakshmikantham V., and Liu X.Z. Nonlinear Integral Equations in Abstract Spaces (1996), Kluwer Academic Publishers, Dordrecht
13. Guo D.J., and Lakshmikantham V. Nonlinear Problems in Abstract Cones (1988), Academic Press, Inc., NewYork
14. Lakshmikanthan V., and Leela S. Nonlinear Differential Equations in Abstract Spaces (1981), Pergamon Oxford
15. Guo D.J. Multiple positive solutions for first order nonlinear impulsive integro-differential equations in a Banachspace. Appl. Math. Comput. 143 (2003) 233-249
16. Ma R., and Wang H. Positive solutions of nonlinear three-point boundary-value problems. J. Math. Anal. Appl. 279 (2003) 216-227
17. Ma R. Positive solutions for second order three-point boundary value problems. Appl. Math. Lett. 14 (2001) 1-5
18. Wei Z., and Pang C. Positive solutions of some singular m-point boundary value problems at nonresonance. Appl. Math. Comput. 171 (2005) 433-449
19. Pang C., Dong W., and Wei Z. Green's function and positive solutions of nth order m-point boundary value problem. Appl. Math. Comput. 182 (2006) 1231-1239
20. Liu Y. Multiple positive solutions to fourth-order singular boundary value problems in abstract space. Electron. J. Differential Equations 2004 120 (2004) 1-13
21. Feng M., and Zhang X. Multiple solutions of two-point boundary value problem of fourth-order ordinary differential equations in Banach space. Acta Anal. Funct. Appl. 6 (2004) 56-64 (in Chinese)
22. Feng M., and Ge W. Positive solutions for a class of m-point singular boundary value problems. Math. Comput. Modelling 46 (2007) 375-383
23. Zhao Y., and Chen H. Existence of multiple positive solutions for m-point boundary value problems in Banach spaces. J. Comput. Appl. Math. (2007). doi:10.1016/j.cam.2007.03.025
24. Liu B. Positive solutions of a nonlinear four-point boundary value problems in Banach spaces. J. Math. Anal. Appl. 305 (2005) 253-276
25. Cheung W., and Ren J. Positive solutions for m-point boundary-value problems. J. Math. Anal. Appl. 303 (2005) 565-575
26. Liu Y., and Ge W. Positive solutions for (n - 1, 1) three-point boundary value problem with coefficient that changes sign. J. Math. Anal. Appl. 282 (2003) 816-825
27. Guo Y. positive solutions for three-point boundary value problems with dependence on the first order derivatives. J. Math. Anal. Appl. 290 (2004) 291-301
28. Guo Y., Shan W., and Ge W. Positive solutions for second-order m-point boundary value problems. J. Comput. Appl. Math. 151 (2003) 415-424
29. Liu X., Qiu J., and Guo Y. Three positive solutions for second-order m-point boundary value problems. Appl. Math. Comput. 156 (2004) 733-742
30. Guo Y., Liu X., and Qiu J. Three positive solutions for higher order m point boundary value problems. J. Math. Anal. Appl. 289 (2004) 545-553
31. Zhang G., and Sun J. Positive solutions of m-point boundary value problems. J. Math. Anal. Appl. 291 (2004) 406-418