On the boundary blow-up solutions of p(x)-Laplacian equations with singular coefficient

Abstract This paper investigates the problem { − Δ p ( x ) u + ρ ( x ) f ( x , u ) = 0 in  Ω , u ( x ) → + ∞ as  d ( x , ∂ Ω ) → 0 , where − Δ p ( x ) u = − div ( | ∇ u | p ( x ) − 2 ∇ u ) is called the p ( x ) -Laplacian, ρ ( x ) is a singular coefficient. The existence and nonexistence of boundary blow-up solutions are discussed, and the singularity of the boundary blow-up solution is given.

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