We use the nonlinear alternative and topological transversality to prove an existence theorem for the solutions of the functional differential equation ẋ(t) = F (t, x t ), where x t (θ ) = x(t + θ ) for all θ ∈ [-r, 0] and F : [0, A] × X 2 → X , X is a Banach space and X 2 is the Banach space of con
An existence result for a superlinear fractional differential equation
✍ Scribed by Dumitru Băleanu; Octavian G. Mustafa; Ravi P. Agarwal
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 250 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
✦ Synopsis
We establish the existence and uniqueness of solution for the boundary value problem
Riemann-Liouville derivative of order α ∈ (0, 1) and λ > 1. Our result might be useful for establishing a non-integer variant of the Atkinson classical theorem on the oscillation of Emden-Fowler equations.
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