| Title:
|
Existence of solutions for a coupled system with $\phi $-Laplacian operators and nonlinear coupled boundary conditions (English) |
| Author:
|
Goli, Konan Charles Etienne |
| Author:
|
Adjé, Assohoun |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
25 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
79-87 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the existence of solutions of the system $$ \begin {cases} (\phi _1(u_1'(t)))'= f_1(t,u_1(t),u_2(t),u'_1(t),u_2'(t)),\qquad \text {a.e. $t\in [0,T]$}, (\phi _2(u_2'(t)))'= f_2(t,u_1(t),u_2(t),u'_1(t),u_2'(t)),\qquad \text {a.e. $t\in [0,T]$}, \end {cases} $$ submitted to nonlinear coupled boundary conditions on $[0,T]$ where $\phi _1,\phi _2\colon (-a, a)\rightarrow \mathbb {R}$, with $0 < a < +\infty $, are two increasing homeomorphisms such that $\phi _1(0) = \phi _2(0) = 0$, and $f_i:[0,T]\times \mathbb {R}^{4}\rightarrow \mathbb {R}$, $i\in \{1,2\}$ are two $L^1$-Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result. (English) |
| Keyword:
|
$\phi $-Laplacian; $L^1$-Carath\'eodory function; Schauder fixed-point Theorem. |
| MSC:
|
34B15 |
| idZBL:
|
Zbl 1391.34052 |
| idMR:
|
MR3745430 |
| . |
| Date available:
|
2018-02-05T14:37:07Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147058 |
| . |
| 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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| . |
