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In this paper, we focus on the existence of positive solutions for nonlinear fourth-order Neumann boundary value problem  where  k1  and  k2  are constants, λ &gt; 0 is the bifurcation parameter,  f  ∈  C ([0, 1] × ℝ + , ℝ), ℝ +  := [0, ∞). We first discuss the sign properties of Green’s function for the elastic beam boundary value problem, and then we show that there exists a global branch of solutions emanating from infinity under some different growth conditions. In addition, we prove that for λ near the bifurcation points, solutions of large norm are indeed positive. The technique for dealing with this paper relies on the global bifurcation theory.

Global structure of positive solutions for semipositone nonlinear Euler-Bernoulli beam equation with Neumann boundary conditions