Construction of Upper and Lower Solutions for Singular Discrete Initial and Boundary Value Problems via Inequality Theory
نویسندگان
چکیده
where φp(s)=|s|p−2s, p > 1, ∆u(k− 1)=u(k)−u(k−1), T∈{1,2, . . .}, N+={0,1, . . . ,T}, and u :N+ →R. Throughout this paper, we will assume f :N × (0,∞)→R is continuous. As a result, our nonlinearity f (k,u) may be singular at u= 0 and may change sign. Remark 1.1. Recall a map f :N × (0,∞)→R is continuous if it is continuous as a map of the topological space N × (0,∞) into the topological space R. Throughout this paper, the topolopy on N will be the discrete topology.
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