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In this paper, we consider the existence of nontrivial solutions for the nonlinear fractional differential equation boundary-value problem (BVP)−Dα0+u(t) = λ[f(t, u(t)) + q(t)], 0 < t < 1u(0) = u(1) = 0,where λ > 0 is a parameter, 1 < α ≤ 2, Dα0+ is the standard Riemann-Liouville differentiation, f : [0, 1] × R → R is continuous, and q(t) :(0, 1) → [0,+∞) is Lebesgue integrable. We obtain serval sufficient conditions of the existence and uniqueness of nontrivial solution of BVP when λ 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.
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참고문헌 (9)
참고문헌 신청
B. Liu / 2002 / Positive solutions of a nonlinear three-point boundary value problem / Comput. Math. Appl. 44 (1) : 201 ~ 211
D. Delbosco / 1996 / Existence and uniqueness for a nonlinear fractional differential equation / J. Math. Anal. Appl. 204 (2) : 609 ~ 625
I. Podlubny / 1999 / Fractional Differential Equations / Academic Press, Inc.
K. Deimling / 1985 / Nonlinear Functional Analysis / Springer-Verlag
O. P. Agrawal / 2002 / Formulation of Euler-Lagrange equations for fractional variational problems / J. Math. Anal. Appl. 272 (1) : 368 ~ 379
D. Delbosco / 1996 / Existence and uniqueness for a nonlinear fractional differential equation / J. Math. Anal. Appl. 204 (2) : 609 ~ 625
I. Podlubny / 1999 / Fractional Differential Equations / Academic Press, Inc.
K. Deimling / 1985 / Nonlinear Functional Analysis / Springer-Verlag
O. P. Agrawal / 2002 / Formulation of Euler-Lagrange equations for fractional variational problems / J. Math. Anal. Appl. 272 (1) : 368 ~ 379
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