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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:
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