In this article, we study the degenerated quasilinear elliptic equations $$\displaylines{ - \hbox{div}(\mathcal{B}(x,\upsilon_{1},D \upsilon_{1}))+g(x,\upsilon_{1}) = f(x) \quad \text{in } \Omega_{1},\cr - \hbox{div}(\mathcal{B}(x,\upsilon_{2},D \upsilon_{2}))+g(x,\upsilon_{2}) = f(x) \quad \text{in } \Omega_{2},\cr \upsilon_1 = 0 \quad \text{on } \partial\Omega ,\cr \mathcal{B}(x,\upsilon_{1},D \upsilon_{1})\cdot \nu_{1} = \mathcal{B}(x,\upsilon_{2},D \upsilon_{2})\cdot \nu_{1} \quad\text{on } \Gamma,\cr \mathcal{B}(x,\upsilon_{1},D \upsilon_{1})\cdot \nu_{1} = - h(x)|\upsilon_{1}-\upsilon_{2}|^{p-2}(\upsilon_{1}-\upsilon_{2}) \quad \text{on } \Gamma, }$$ where \(\Omega\) is a connected bounded open set of \(\mathbb{R}^N\) (\(N\geq 2\)), and can be decomposed as \( \Omega = \Omega_{1} \cup \Omega_{2}\cup\Gamma\), where \(\Omega_{2}\) is an open subset included in \(\Omega\), and \(\Omega_{1}=\Omega \setminus\overline{\Omega_{2}}\) and \(\Gamma = \partial\Omega_{2}\), with \(2+\lambda-\frac{1}{N}< p
Math Subject Classifications: 35J60, 46E30, 46E35.
Key Words: Degenerated quasilinear elliptic equations; two-component domain; entropy solutions
DOI: 10.58997/ejde.2026.42
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Youssef Hajji Department of Mathematics Faculty of Sciences T&eacutte;touan University Abdelmalek Essaadi BP 2121, T&eacutte;touan, Morocco email: youssef.hajji@etu.uae.ac.ma |
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Hassane Hjiaj Department of Mathematics Faculty of Sciences T&eacutte;touan University Abdelmalek Essaadi BP 2121, T&eacutte;touan, Morocco email: hjiajhassane@yahoo.fr |
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Ismail Jamiai Laboratoire LAR2A Department of Mathematics Faculty of Sciences T&eacutte;touan University Abdelmalek Essaadi BP 2121, T&eacutte;touan, Morocco email: ijamiai@uae.ac.ma |
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Mohamed Yarmak Department of Mathematics Faculty of Sciences T&eacutte;touan University Abdelmalek Essaadi BP 2121, T&eacutte;touan, Morocco email: mohamed.yarmak@etu.uae.ac.ma |
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