Existence of solutions for a coupled system with $\phi$-Laplacian operators and nonlinear coupled boundary conditions

Goli, Konan Charles Etienne, and Adjé, Assohoun. "Existence of solutions for a coupled system with $\phi $-Laplacian operators and nonlinear coupled boundary conditions." Communications in Mathematics 25.2 (2017): 79-87. <http://eudml.org/doc/294643>.

@article{Goli2017,
abstract = {We study the existence of solutions of the system \[ \{\left\lbrace \begin\{array\}\{ll\} (\phi \_1(u\_1^\{\prime \}(t)))^\{\prime \}= f\_1(t,u\_1(t),u\_2(t),u^\{\prime \}\_1(t),u\_2^\{\prime \}(t)),\qquad \text\{a.e. $t\in [0,T]$\}, (\phi \_2(u\_2^\{\prime \}(t)))^\{\prime \}= f\_2(t,u\_1(t),u\_2(t),u^\{\prime \}\_1(t),u\_2^\{\prime \}(t)),\qquad \text\{a.e. $t\in [0,T]$\}, \end\{array\}\right.\} \] 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 \lbrace 1,2\rbrace $ are two $L^1$-Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result.},
author = {Goli, Konan Charles Etienne, Adjé, Assohoun},
journal = {Communications in Mathematics},
keywords = {$\phi $-Laplacian; $L^1$-Carathéodory function; Schauder fixed-point Theorem},
language = {eng},
number = {2},
pages = {79-87},
publisher = {University of Ostrava},
title = {Existence of solutions for a coupled system with $\phi $-Laplacian operators and nonlinear coupled boundary conditions},
url = {http://eudml.org/doc/294643},
volume = {25},
year = {2017},
}

TY - JOUR
AU - Goli, Konan Charles Etienne
AU - Adjé, Assohoun
TI - Existence of solutions for a coupled system with $\phi $-Laplacian operators and nonlinear coupled boundary conditions
JO - Communications in Mathematics
PY - 2017
PB - University of Ostrava
VL - 25
IS - 2
SP - 79
EP - 87
AB - We study the existence of solutions of the system \[ {\left\lbrace \begin{array}{ll} (\phi _1(u_1^{\prime }(t)))^{\prime }= f_1(t,u_1(t),u_2(t),u^{\prime }_1(t),u_2^{\prime }(t)),\qquad \text{a.e. $t\in [0,T]$}, (\phi _2(u_2^{\prime }(t)))^{\prime }= f_2(t,u_1(t),u_2(t),u^{\prime }_1(t),u_2^{\prime }(t)),\qquad \text{a.e. $t\in [0,T]$}, \end{array}\right.} \] 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 \lbrace 1,2\rbrace $ are two $L^1$-Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result.
LA - eng
KW - $\phi $-Laplacian; $L^1$-Carathéodory function; Schauder fixed-point Theorem
UR - http://eudml.org/doc/294643
ER -