Abstract. In this paper, we are concerned with the global structure of radial positive solutions of boundary value problemN , λ is a positive parameter, B(R) = {x ∈ R N : |x| < R}, and | · | denote the Euclidean norm in R N . All results, depending on the behavior of nonlinear term f near 0, are obtained by using global bifurcation techniques.
We prove the existence of one-signed periodic solutions of second-order nonlinear difference equation on a finite discrete segment with periodic boundary conditions by combining some properties of Green's function with the fixed-point theorem in cones.
we show the existence and multiplicity of positive solutions of the nonlinear discrete fourth-order boundary value problemΔ4ut-2=λhtfut,t∈T2,u1=uT+1=Δ2u0=Δ2uT=0, whereλ>0,h:T2→(0,∞)is continuous, andf:R→[0,∞)is continuous,T>4,T2=2,3,…,T. The main tool is the Dancer's global bifurcation theorem.
We study one-signed periodic solutions of the first-order functional differential equationω 0 b t dt > 0, τ is a continuous ω-periodic function, and λ > 0 is a parameter. f ∈ C R,R and there exist two constants s 2 < 0 < s 1 such that f s 2 f 0 f s 1 0, f s > 0 for s ∈ 0, s 1 ∪ s 1 , ∞ and f s < 0 for s ∈ −∞, s 2 ∪ s 2 , 0 .
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