A strong maximum principle for differential equations with nonstandard p(x)-growth conditions

Abstract In this paper, with some special technics, we give a strong maximum principle for the equations with nonstandard p ( x ) -growth conditions − div ( φ ( x , | ∇ u | ) ∇ u ) + d ( x ) f ( x , u ) = 0 in  Ω , where φ ( x , s ) , d ( x ) , f ( x , u ) satisfy some conditions.

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