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- W1975548849 abstract "Abstract In this article, we study the existence of positive weak solution for a class of ( p , q ) -Laplacian system { − Δ p u = λ a ( x ) f ( v ) , x ∈ Ω , − Δ q v = λ b ( x ) g ( u ) , x ∈ Ω , u = v = 0 , x ∈ ∂ Ω , where Δ p denotes the p-Laplacian operator defined by Δ p z = d i v ( ∣ ∇ z ∣ p − 2 ∇ z ) , p > 1 , λ > 0 is a parameter and Ω is a bounded domain in R N ( N > 1 ) with smooth boundary ∂ Ω . Here a ( x ) and b ( x ) are C 1 sign-changing functions that maybe negative near the boundary and f , g are C 1 nondecreasing functions such that f , g : [ 0 , ∞ ) → [ 0 , ∞ ) ; f ( s ) , g ( s ) > 0 ; s > 0 and for every M > 0 , lim x → ∞ f ( M g ( x ) 1 q − 1 ) x p − 1 = 0 . We discuss the existence of positive weak solution when f , g , a ( x ) and b ( x ) satisfy certain additional conditions. We use the method of sub–supersolutions to establish our results." @default.
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- W1975548849 date "2010-07-01" @default.
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- W1975548849 title "A remark on the existence of positive weak solution for a class of -Laplacian nonlinear system with sign-changing weight" @default.
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- W1975548849 doi "https://doi.org/10.1016/j.na.2010.03.027" @default.
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