Existence theory for perturbed nonlinear boundary value problems with integral boundary conditions

Georgian Mathematical Journal

Volumn 13, Issue 2, 2006, Pages 215-228

  Belarbi, Abdelkader ^a   Benchohra, Mouffak ^a   Dhage, Bapurao C ^b  

^a UNIVERSITY OF SIDI BEL ABBES   (Algeria)

^b Kasubai   (India)

Author keywords

extremal solutions; fixed point; Nonlinear boundary value problem

Indexed keywords

EID: 77949268160     PISSN: 1072947X     EISSN: 15729176     Source Type: Journal    
DOI: 10.1515/GMJ.2006.215     Document Type: Article

References (20)

1. J.-P. AUBIN and A. CELLINA, Differential inclusions. Set-valued maps and viability theory. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 264. Springer-Verlag, Berlin, 1984.
2. J.-P. AUBIN and H. FRANKOWSKA, Set-valued analysis. Systems & Control: Foundations & Applications, 2. Birkhauser Boston, Inc., Boston, MA, 1990.
3. A. BELARBI and M. BENCHOHRA, Existence results for nonlinear boundary-value problems with integral boundary conditions. Electron. J. Differential Equations 2005, No. 06, 10 pp. (electronic).
4. S. A. BRYKALOY, A Second-order nonlinear problem with two-point and integral boundary conditions. Georgian Math. J. 1(1994), No. 3, 243-249.
5. C. CASTAING and M. VALADIER, Convex analysis and measurable multifunctions. Lecture Notes in Mathematics, Vol. 580. Springer-Verlag, Berlin-New York, 1977.
6. K. DEIMLING, Multivalued differential equations. de Gruyter Series in Nonlinear Analysis and Applications, 1. Walter de Gruyter & Co., Berlin, 1992.
7. M. DENCHE and A. L. MARHOUNE, High-order mixed-type differential equations with weighted integral boundary conditions. Electron. J. Differential Equations 2000, No. 60, 10 pp. (electronic).
8. B. C. DHAGE, Multivalued mappings and fixed points. II. Tamkang J. Math. 36(2006) (to appear).
9. B.C. DHAGE, A fixed point theorem for multi-valued mappings in ordered Banach spaces with applications. II. Panamer. Math. J. 15(2005), No. 3, 15-34.
10. B. C. DHAGE, E. GATSORI, and S. K. NTOUYAS, Existence theory for perturbed functional differential inclusions. Med. J. Math. (to appear).
11. J. M. GALLARDO, Second-order differential operators with integral boundary conditions and generation of analytic semigroups. Rocky Mountain J. Math. 30(2000), No. 4, 1265-1291.
12. S. HEIKKILA and V. LAKSHMIKANTHAM, V. Monotone iterative techniques for discontinuous nonlinear differential equations. Monographs and Textbooks in Pure and Applied Mathematics, 181. Marcel Dekker, Inc., New York, 1994.
13. SH. HU and N. S. PAPAGEORGIOU, Handbook of multivalued analysis. Vol. I. Theory. Mathematics and its Applications, 419. Kluwer Academic Publishers, Dordrecht, 1997.
14. T. JANKOWSKII, Differential equations with integral boundary conditions. J. Comput. Appl. Math. 147(2002), No. 1, 1-8.
15. G. L. KARAKOSTAS and P. CH. TSAMATOS, Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary-value problems. Electron. J. Differential Equations 2002, No. 30, 17 pp. (electronic).
16. R. A. KHAN, The generalized method of quasilinearization and nonlinear boundary value problems with integral boundary conditions. Electron. J. Qual. Theory Differ. Equ. 2003, No. 19, 15 pp. (electronic).
17. M. KISIELEWICZ, Differential inclusions and optimal control. Mathematics and its Applications (East European Series), 44. Kluwer Academic Publishers Group, Dordrecht; PWN’Polish Scientific Publishers, Warsaw, 1991.
18. A. M. KRALL, The adjoint of a differential operator with integral boundary conditions. Proc. Amer. Math. Soc. 16(1965), 738-742.
19. A. LASOTA and Z. OPIAL, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull. Acad. Polon. Sci. Sr. Sci. Math. Astronom. Phys. 13(1965), 781-786.
20. A. LOMTATIDZE and L. MALAGUTI, On a nonlocal boundary value problem for second order nonlinear singular differential equations. Georgian Math. J. 7(2000), No. 1, 133-154.