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Nontrivial solutions for a nonlinear multi-point boundary value problem of fractional order. (English) Zbl 1197.34003
Summary: We investigate the existence of nontrivial solutions for a multi-point boundary value problem for fractional differential equations. Under certain growth conditions on the nonlinearity, several sufficient conditions for the existence of nontrivial solution are obtained by using Leray-Schauder nonlinear alternative. As an application, some examples to illustrate our results are given.
MSC:
34A08Fractional differential equations
34B10Nonlocal and multipoint boundary value problems for ODE
45J05Integro-ordinary differential equations
References:
[1]Das, S.: Functional fractional calculus for system identification and controls, (2008)
[2]Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, (2006)
[3]Podlubny, J.: Fractional differential equations, (1999)
[4]Ahmad, B.; Nieto, J. J.: Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations, Abstract and applied analysis 2009, 1-9 (2009)
[5]Ahmad, B.; Nieto, J. J.: Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Computers and mathematics with applications 58, 1838-1843 (2009) · Zbl 1205.34003 · doi:10.1016/j.camwa.2009.07.091
[6]Belmekki, M.; Nieto, J. J.; Rodriguez-Lopez, R.: Existence of periodic solution for a nonlinear fractional differential equation, Boundary value problems 2009, 1-18 (2009) · Zbl 1181.34006 · doi:10.1155/2009/324561
[7]Chang, Y.; Nieto, J. J.: Some new existence results for fractional differential inclusions with boundary conditions, Mathematical and computer modelling 49, 605-609 (2009) · Zbl 1165.34313 · doi:10.1016/j.mcm.2008.03.014
[8]Lakshmikantham, V.; Leela, S.: Nagumo-type uniqueness result for fractional differential equations, Nonlinear analysis 71, 2886-2889 (2009) · Zbl 1177.34003 · doi:10.1016/j.na.2009.01.169
[9]Odibat, Z.; Momani, S.: A generalized differential transform method for linear partial differential equations of fractional order, Applied mathematics letters 21, 194-199 (2008) · Zbl 1132.35302 · doi:10.1016/j.aml.2007.02.022
[10]Rivero, M.; Rodriguez-Germa, L.; Trujillo, J. J.: Linear fractional differential equations with variable coefficients, Applied mathematics letters 21, 892-897 (2008) · Zbl 1152.34305 · doi:10.1016/j.aml.2007.09.010
[11]Guerekata, G. M.: Cauchy problem for some fractional abstract differential equation with non local conditions, Nonlinear analysis 70, 1873-1876 (2009) · Zbl 1166.34320 · doi:10.1016/j.na.2008.02.087
[12]Li, C. F.; Luo, X. N.; Zhou, Y.: Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Computers and mathematics with applications 59, 1363-1375 (2010) · Zbl 1189.34014 · doi:10.1016/j.camwa.2009.06.029
[13]Il’in, V. A.; Moiseev, E. I.: Nonlocal boundary value problem of the second kind for a Sturm Liouville operator, Differential equations 23, No. 8, 979-987 (1987) · Zbl 0668.34024
[14]Il’in, V. A.; Moiseev, E. I.: Nonlocal boundary value problem of the first kind for a Sturm Liouville operator in its differential and finite difference aspects, Differential equations 23, No. 7, 803-810 (1987) · Zbl 0668.34025
[15]Guo, Y.; Ji, Y.; Zhang, J.: Three positive solutions for a nonlinear nth-order m-point boundary value problem, Nonlinear analysis 68, 3485-3492 (2007) · Zbl 1156.34311 · doi:10.1016/j.na.2007.03.041
[16]Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones, (1988)