Phân tích tư tưởng của nhân dân qua đoạn thơ: Những người vợ nhớ chồng… Những cuộc đời đã hóa sông núi ta trong Đất nước của Nguyễn Khoa Điềm
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CONSTRUCTION OF UPPER AND LOWER SOLUTIONS FOR SINGULAR DISCRETE INITIAL AND BOUNDARY VALUE PROBLEMS VIA INEQUALITY THEORY¨ HAISHEN LU AND DONAL O’REGAN Received 25 May 2004We present new existence results for singular discrete initial and boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign. 1. Introduction An upper- and lower-solution theory is presented for the singular discrete boundary value problem−∆ ϕ p ∆u(k − 1) = q(k) f k,u(k) ,k ∈ N = {1,...,T },u(0) = u(T + 1) = 0, and the singular discrete initial value problem ∆u(k...
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CONSTRUCTION OF UPPER AND LOWER SOLUTIONS FOR SINGULAR DISCRETE INITIAL AND BOUNDARY VALUE PROBLEMS
