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Existence of solutions to a non‐variational singular elliptic system with unbounded weights
Author(s) -
Cave L. M.,
Oliva F.,
Strani M.
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600038
Subject(s) - mathematics , bounded function , lebesgue integration , operator (biology) , laplace operator , pure mathematics , p laplacian , open set , mathematical analysis , set (abstract data type) , biochemistry , chemistry , repressor , computer science , transcription factor , programming language , gene , boundary value problem
In this paper we prove an existence result for the following singular elliptic systemz > 0 in Ω , z ∈ W 0 1 , p( Ω ):− Δ p z = a ( x ) z q − 1u θ,u > 0 in Ω , u ∈ W 0 1 , p( Ω ):− Δ p u = b ( x ) z q u θ − 1,where Ω is a bounded open set in error N ( N ≥ 2 ), − Δ pis the p ‐laplacian operator, a ( x ) and b ( x ) are suitable Lebesgue functions and q > 0 , 0 < θ < 1 , p > 1 are positive parameters satisfying suitable assumptions.