Positive solutions of functional difference equations with p-Laplacian operator
نویسندگان
چکیده
منابع مشابه
Existence of Positive Solutions for Boundary Value Problems of Nonlinear Functional Difference Equation with p-Laplacian Operator
In recent years, boundary value problems of differential and difference equations have been studied widely and there are many excellent results (see Erbe and Wang [1], Grimm and Schmitt [2], Gustafson and Schmitt [3], Weng and Jiang [4], Weng and Tian [5], Wong [6], and Yang et al. [7]). Weng and Guo [8] considered two-point boundary value problem of a nonlinear functional difference equation w...
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where • N > an integer; • a, c > , and b,d ≥ with ad + ac(N + ) + bc > ; • f and q are continuous and positive; • φp is called p-Laplacian, φp(x) = |x|p–x with p > , its inverse function is denoted by φq(x) with φq(x) = |x|q–x with /p + /q = ; • ∑s i=r x(i) = if r, s ∈ Z and s < r, where Z is the integer set, denote [r, s] = {r, r + , . . . , s} for r, s ∈ Z with r ≤ s. Differen...
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Let Ω be a domain in Rd, d ≥ 2, and 1 < p < ∞. Fix V ∈ Lloc(Ω). Consider the functional Q and its Gâteaux derivative Q′ given by Q(u) := 1 p ∫ Ω (|∇u|+V |u|)dx, Q(u) :=−∇· (|∇u|∇u)+V |u|u. In this paper we discuss several aspects of relations between functionalanalytic properties of the functional Q and properties of positive solutions of the equation Q′(u) = 0. 2000 Mathematics Subject Classif...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2006
ISSN: 1687-1839,1687-1847
DOI: 10.1155/ade/2006/82784