| Title:
|
Existence Results for a Fractional Boundary Value Problem via Critical Point Theory (English) |
| Author:
|
Boucenna, A. |
| Author:
|
Moussaoui, T. |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
47-64 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we consider the following boundary value problem \[ \left\lbrace \begin{array}{lll} D_{T^{-}}^{\alpha } (D_{0^{+}}^{\alpha } (D_{T^{-}}^{\alpha }(D_{0^{+}}^{\alpha } u(t))) ) = f(t, u(t)), \quad t \in [0, T], \\ u(0)= u(T)= 0\\ D_{T^{-}}^{\alpha }(D_{0^{+}}^{\alpha }u(0))= D_{T^{-}}^{\alpha }(D_{0^{+}}^{\alpha }u(T))= 0, \end{array} \right. \] where $0 < \alpha \le 1$ and $f\colon [0, T]\times \mathbb {R} \rightarrow \mathbb {R} $ is a continuous function, $D_{0^{+}}^{\alpha }$, $D_{T^{-}}^{\alpha }$ are respectively the left and right fractional Riemann–Liouville derivatives and we prove the existence of at least one solution for this problem. (English) |
| Keyword:
|
Existence results |
| Keyword:
|
fractional differential equation |
| Keyword:
|
boundary value problem |
| Keyword:
|
critical point theory |
| Keyword:
|
minimization principle |
| Keyword:
|
Mountain pass theorem |
| Keyword:
|
Third order |
| Keyword:
|
nonlinear differential equation |
| Keyword:
|
uniform stability |
| Keyword:
|
uniform ultimate boundedness |
| Keyword:
|
periodic solutions |
| MSC:
|
26A33 |
| MSC:
|
34B15 |
| MSC:
|
58E05 |
| idZBL:
|
Zbl 1354.34013 |
| idMR:
|
MR3468600 |
| . |
| Date available:
|
2015-09-01T08:58:50Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144367 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
