论文信息 - NONTRIVIAL SOLUTIONS FOR BOUNDARY-VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

NONTRIVIAL SOLUTIONS FOR BOUNDARY-VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

In this paper, we consider the existence of nontrivial solutions for the nonlinear fractional dierential equation boundary-value problem (BVP) iD fiu(t) = ‚(f(t,u(t)) + q(t)), 0 < t < 1 con- ditions of the existence and uniqueness of nontrivial solution of BVP when ‚ in some interval. Our approach is based on Leray-Schauder nonlinear alternative. Particularly, we do not use the nonnegative assumption and monotonicity which was essential for the technique used in almost all existed literature on f.

Yingxin Guo

[1] Bing Liu. Positive solutions of a nonlinear three-point boundary value problem , 2002, Appl. Math. Comput..

[2] Luigi Rodino,et al. Existence and Uniqueness for a Nonlinear Fractional Differential Equation , 1996 .

[3] K. Deimling. Nonlinear functional analysis , 1985 .

[4] Shuqin Zhang,et al. Existence of positive solution for some class of nonlinear fractional differential equations , 2003 .

[5] O. Marichev,et al. Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[6] R. Ma,et al. Positive solutions of a nonlinear three-point boundary-value problem. , 1999 .

[7] Shuqin Zhang,et al. The Existence of a Positive Solution for a Nonlinear Fractional Differential Equation , 2000 .

[8] Tingting Qiu,et al. Positive solutions for boundary value problem of nonlinear fractional differential equation. , 2008 .

[9] Om P. Agrawal,et al. Formulation of Euler–Lagrange equations for fractional variational problems , 2002 .

[10] I. Podlubny. Fractional differential equations , 1998 .

[11] Varsha Daftardar-Gejji,et al. Existence of positive solutions of nonlinear fractional differential equations , 2003 .