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In this article, we consider the equation

with ai(x), pi(x) ∈ C1 (Ω) and pi(x) > 1. Where ai(x) = 0 if x ∈ ∂Ω, and ai(x) > 0 if x ∈ Ω, without any boundary conditions. We propose an analytical method for studying the stability of weak solutions. We also study the uniqueness of a weak solution, and establish its stability under certain conditions.

Publication Title

Electronic Journal of Differential Equations

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Mathematics Commons



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