Da-Bin Wang

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In this paper, by using Guo-Krasnosel'skii fixed point theorem in cones, we study the existence, multiplicity and infinite solvability of positive solutions for the following three-point boundary value problems for p-Laplacian dynamic equations on time scales [Φp(u (t))] + a(t)f (t, u(t)) = 0, t ∈ [0, T ] T , u(0) − B 0 (u (η)) = 0, u (T) = 0. By(More)
By using the fixed point theorem in cones, in this paper, existence criteria for single and multiple positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales are obtained. An example is given to illustrate the main results in this article.
In this paper, we establish the existence of three positive solutions to the following p-Laplacian functional dynamic equation on time scales, [Φp(u ∆ (t))] ∇ + a(t)f (u(t), u(µ(t))) = 0, t ∈ (0, T) T , u 0 (t) = ϕ(t), t ∈ [−r, 0] T , u(0) − B 0 (u ∆ (η)) = 0, u ∆ (T) = 0,. using the fixed-point theorem due to Avery and Peterson [8]. An example is given to(More)
In this paper, we consider the following dynamic system with parameter on a measure chain T, u ∆∆ i (t) + λh i (t)f i (u 1 (σ(t)), u 2 (σ(t)),. .. , un(σ(t))) = 0, t ∈ [a, b], αu i (a) − βu ∆ i (a) = 0, γu i (σ(b)) + δu ∆ i (σ(b)) = 0, where i = 1, 2,. .. , n. Using fixed-point index theory, we find sufficient conditions the existence of positive solutions.
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