Solvability of boundary-value problems for nonlinear fractional differential equations
We consider the existence of nontrivial solutions of the boundary-value problems for nonlinear fractional differential equations Dαu(t) + λ[f(t,u(t)) + q(t)]=0, 0 < t < 1, u(0) = 0, u(1) = βu(η), where λ > 0 is a parameter, 1 < α ≤ 2, η ∈ (0, 1), β∈R=(−∞,+∞), βη α−1 ≠ 1, Dα is a Riem...
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| Дата: | 2010 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2010
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| Назва видання: | Український математичний журнал |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/166286 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Solvability of boundary-value problems for nonlinear fractional differential equations / Y. Guo // Український математичний журнал. — 2010. — Т. 62, № 9. — С. 1211–1219. — Бібліогр.: 13 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We consider the existence of nontrivial solutions of the boundary-value problems for nonlinear fractional differential equations
Dαu(t) + λ[f(t,u(t)) + q(t)]=0, 0 < t < 1, u(0) = 0, u(1) = βu(η),
where λ > 0 is a parameter, 1 < α ≤ 2, η ∈ (0, 1), β∈R=(−∞,+∞), βη α−1 ≠ 1, Dα is a Riemann–Liouville differential operator of order α, f:(0,1)×R→R is continuous, f may be singular for t = 0 and/or t = 1, and q(t) : [0, 1] → [0, +∞) We give some sufficient conditions for the existence of nontrivial solutions to the formulated boundary-value problems. Our approach is based on the Leray–Schauder nonlinear alternative. In particular, we do not use the assumption of nonnegativity and monotonicity of f essential for the technique used in almost all available literature. |
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