Renata Wieteska

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In this paper we consider the Dirichlet problem for a discrete anisotropic equation with some function α , a nonlinear term f , and a numerical parameter λ : ∆ ( α (k) |∆u(k − 1)|p(k−1)−2∆u(k − 1) ) + λf(k, u(k)) = 0, k ∈ [1, T ] . We derive the intervals of a numerical parameter λ for which the considered BVP has at least 1, exactly 1, or at least 2(More)
where T ≥ 2 is an integer, ∆ is the forward difference operator defined by ∆u(k) = u(k + 1) − u(k), u (k) ∈ R for all k ∈ N(1, T ), for fixed a, b such that a < b < ∞, a ∈ N∪{0}, b ∈ N we denote N(a, b) = {a, a+1, . . . , b−1, b}, f : N(1, T )×R×W→ R, w ∈ W, the space W is some topological space (in most applications one takes R in place of W), p : N(0, T(More)
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