Details

Autor(en) / Beteiligte

• Phung, Phan Dinh
• Minh, Ha Binh

Titel

Existence of solutions to fractional boundary value problems at resonance in Hilbert spaces

Ist Teil von

• Boundary value problems, 2017-07, Vol.2017 (1), p.1-20, Article 105

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2017

Quelle

Springer Nature - Complete Springer Journals

Beschreibungen/Notizen

• We study the existence of solutions to a nonlinear fractional differential equation in Hilbert spaces associated with three-point boundary conditions at resonance x ( 0 ) = θ , D α − 1 x ( 1 ) = A D α − 1 x ( η ) by using Mawhin’s continuation theorem. We propose a new technique to improve the conditions on A which have been used previously. In addition, a necessary and sufficient condition for that the fractional differential operator is Fredholm with zero-index is established, especially for the first time when the fractional differential operator takes values in an arbitrary Hilbert space.