Previous |  Up |  Next

Article

Keywords:
multiple solutions; Leggett-Williams fixed point theorem; nonlinear boundary value problem; integral boundary conditions
Summary:
In this paper we investigate the existence of multiple positive solutions for nonlinear boundary value problems with integral boundary conditions. We shall rely on the Leggett-Williams fixed point theorem.
References:
[1] Agarwal, R. P., O’Regan, D.: Existence of three solutions to integral and discrete equations via the Leggett-Williams fixed point theorem. Rocky Mountain J. Math. 31 (2001), 23–35. DOI 10.1216/rmjm/1008959665 | MR 1821365 | Zbl 0979.45003
[2] Agarwal, R. P., O’Regan, D., Wong, P. J. Y.: Positive Solutions of Differential, Difference and Integral Equations. Kluwer Academic Publishers, Dordrecht, 1999. MR 1680024
[3] Ahmad, B, Khan, R. A., Sivasundaram, S.: Generalized quasilinearization method for a first order differential equation with integral boundary condition. Dynam. Contin. Discrete Impuls. Systems, Ser. A Math. Anal. 12 (2005), 289–296. MR 2170414 | Zbl 1084.34007
[4] Anderson, D., Avery, R., Peterson, A.: Three positive solutions to a discrete focal boundary value problem. Positive solutions of nonlinear problems. J. Comput. Appl. Math. 88 (1998), 103–118. DOI 10.1016/S0377-0427(97)00201-X | MR 1609058
[5] Brykalov, S. A.: A second order nonlinear problem with two-point and integral boundary conditions. Georgian Math. J. 1 (1994), 243–249. DOI 10.1007/BF02254673 | Zbl 0807.34021
[6] Denche, M., Marhoune, A. L.: High-order mixed-type differential equations with weighted integral boundary conditions. Electron. J. Differential Equations 60 (2000), 1–10. MR 1787207 | Zbl 0967.35101
[7] Gallardo, J. M.: Second-order differential operators with integral boundary conditions and generation of analytic semigroups. Rocky Mountain J. Math. 30 (2000), 265–1291. MR 1810167 | Zbl 0984.34014
[8] Guo, D., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones. Academic Press, San Diego, 1988. MR 0959889 | Zbl 0661.47045
[9] Karakostas, G. L., Tsamatos, P. Ch.: Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary-value problems. Electron. J. Differential Equations 30 (2002), 17. MR 1907706 | Zbl 0998.45004
[10] Khan, R. A.: The generalized method of quasilinearization and nonlinear boundary value problems with integral boundary conditions. Electron. J. Qual. Theory Differ. Equ. 19 (2003), 15. MR 2039793 | Zbl 1055.34033
[11] Krall, A. M.: The adjoint of a differential operator with integral boundary condition. Proc. Amer. Math. Soc. 16 (1965), 738–742. DOI 10.1090/S0002-9939-1965-0181794-9 | MR 0181794
[12] Leggett, R. W., Williams, L.R.: Multiple positive fixed points of nonlinear operators on ordered Banach spaces. Indiana Univ. Math. J. 28 (1979), 673–688. DOI 10.1512/iumj.1979.28.28046 | MR 0542951 | Zbl 0421.47033
[13] Lomtatidze, A., Malaguti, L.: On a nonlocal boundary value problem for second order nonlinear singular differential equations. Georgian Math. J. 7 (2000), 133–154. MR 1768050 | Zbl 0967.34011
Partner of
EuDML logo