Existence result of second-order differential equations with integral boundary conditions at resonance

Journal of Mathematical Analysis and Applications

Volumn 353, Issue 1, 2009, Pages 311-319

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

^a NORTH CHINA ELECTRIC POWER UNIVERSITY   (China)

^b BEIJING INFORMATION SCIENCE AND TECHNOLOGY UNIVERSITY   (China)

^c BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Coincidence degree theory; Integral boundary conditions; Resonance

Indexed keywords

EID: 58149218134     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.11.082     Document Type: Article

References (39)

1. Gallardo J.M. Second order differential operators with integral boundary conditions and generation of semigroups. Rocky Mountain J. Math. 30 (2000) 1265-1292
2. Karakostas G.L., and Tsamatos P.Ch. Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary-value problems. Electron. J. Differential Equations 30 (2002) 1-17
3. Lomtatidze A., and Malaguti L. On a nonlocal boundary-value problems for second-order nonlinear singular differential equations. Georgian Math. J. 7 (2000) 133-154
4. Ewing R.E., and Lin T. A class of parameter estimation techniques for fluid flow in porous media. Adv. Water Resour. 14 (1991) 89-97
5. Formaggia L., Nobile F., Quarteroni A., and Veneziani A. Multiscale modelling of the circulatory system: A preliminary analysis. Comput. Vis. Sci. 2 (1999) 75-83
6. Shi P. Weak solution to evolution problem with a nonlocal constraint. SIAM J. Anal. 24 (1993) 46-58
7. Formaggia L., Nobile F., Quarteroni A., and Veneziani A. Multiscale modelling of the circulatory system: A preliminary analysis. Comput. Vis. Sci. 2 (1999) 75-83
8. Taylor C., Hughes T., and Zarins C. Finite element modeling of blood flow in arteries. Comput. Methods Appl. Mech. Engrg. 158 (1998) 155-196
9. Womersley J.R. Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127 (1955) 553-563
10. Nicoud F., and Schfonfeld T. Integral boundary conditions for unsteady biomedical CFD applications. Internat. J. Numer. Methods Fluids 40 (2002) 457-465
11. Batten Jr. G.W. Second-order correct boundary conditions for the numerical solution of the mixed boundary problem for parabolic equations. Math. Comp. 17 (1963) 405-413
12. Bouziani A., and Benouar N.E. Mixed problem with integral conditions for a third order parabolic equation. Kobe J. Math. 15 (1998) 47-58
13. Feng M., Ji D., and Ge W. Positive solutions for a class of boundary value problem with integral boundary conditions in Banach spaces. J. Comput. Appl. Math. 222 (2008) 351-363
14. Zhang X., Feng M., and Ge W. Existence results for nonlinear boundary-value problems with integral boundary conditions in Banach spaces. Nonlinear Anal. 69 (2008) 3310-3321
15. Ahmad B., Alsaedi A., and Alghamdi B.S. Analytic approximation of solutions of the forced duffing equation with integral boundary conditions. Nonlinear Anal. Real World Appl. 9 (2008) 1727-1740
16. Zhang X., and Liu L. A necessary and sufficient condition of positive solutions for fourth order multi-point boundary value problem with p-Laplacian. Nonlinear Anal. 68 (2008) 3127-3137
17. Infante G., and Webb J.R.L. Nonlinear non-local boundary-value problems and perturbed hammerstein integral equations. Proc. Edinb. Math. Soc. 49 (2006) 637-656
18. Ma R., and Castaneda N. Existence of solutions of nonlinear m-point boundary value problems. J. Math. Anal. Appl. 256 (2001) 556-567
19. Webb J.R.L., and Infante G. Positive solutions of nonlocal boundary value problems involving integral conditions. Nonlinear Differential Equations Appl. 15 (2008) 45-67
20. Yang Z. Positive solutions to a system of second-order nonlocal boundary value problems. Nonlinear Anal. 62 (2005) 1251-1265
21. Gupta C.P. A second-order m-point boundary value problems at resonance. Nonlinear Anal. 24 (1995) 1483-1489
22. Feng W., and Webb J.R.L. Solvability of three-point boundary value problems at resonance. Nonlinear Anal. 30 (1997) 3227-3238
23. Liu B., and Yu J. Solvability of multi-point boundary value problem at resonance (III). Appl. Math. Comput. 129 (2002) 119-143
24. Gupta C.P. Solvability of multi-point boundary value problem at resonance. Results Math. 28 (1995) 270-276
25. Gupta C.P. Existence theorems for a second-order m-point boundary value problem at resonance. Int. J. Math. Sci. 18 (1995) 705-710
26. 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
27. Liu B. Solvability of multi-point boundary value problem at resonance (II). Appl. Math. Comput. 136 (2003) 353-377
28. Liu B., and Yu J. Solvability of multi-point boundary value problem at resonance (I). Indian J. Pure Appl. Math. 33 (2002) 475-494
29. Su J., and Zhao L. Multiple periodic solutions of ordinary differential equations with double resonance. Nonlinear Anal. (2008) 10.1016/j.na.2008.02.031
30. Rachankove I., and Staněk S. Topological degree method in functional boundary value problems at resonance. Nonlinear Anal. 27 (1996) 271-285
31. Mawhin J. Topological Degree Methods in Nonlinear Boundary Value Problems. CBMS-NSF Regional Conf. Ser. in Math. (1979), American Mathematical Society, Providence, RI
32. Ma R.Y. Multiplicity results for a third order boundary value problem at resonance. Nonlinear Anal. 32 (1998) 493-499
33. Nagle R.K., and Pothoven K.L. On a third-order nonlinear boundary value problems at resonance. J. Math. Anal. Appl. 195 (1995) 148-159
34. Gupta C.P. On a third-order boundary value problem at resonance. Differential Integral Equations 2 (1989) 1-12
35. Du Z., Lin X., and Ge W. On a third order multi-point boundary value problem at resonance. J. Math. Anal. Appl. 302 (2005) 217-229
36. Du Z., Lin X., and Ge W. Some higher order multi-point boundary value problem at resonance. J. Comput. Appl. Math. 177 (2005) 55-65
37. Kuo C. Solvability of a nonlinear two-point boundary value problems at resonance. J. Differential Equations 140 (1997) 1-9
38. Kuo C. Solvability of a nonlinear two-point boundary value problem at resonance II. Nonlinear Anal. 54 (2003) 565-573
39. Krasnosel'skii A.M., and Mawhin J. On some higher order boundary value problems at resonance. Nonlinear Anal. 24 (1995) 1141-1148