On the results of a class of Laplacian problems with Neumann boundary conditions

G Afrouzi, M Moghaddam
2008 UK World Journal of Modelling and Simulation   unpublished
In this paper we study the following Neumann boundary value problem −u (x) = f (λ, u(x)), x ∈ (0, 1), u (0) = 0 = u (1) where λ > 0 is a parameter and f (λ, u(x)) = u 2 (x)−λ. We study the existence and nonexistence of solutions of this problem with respect to a parameter ρ (i.e. u(0) = ρ) in all R. By using a quadrature method, we obtain our results. Also we provide some details about the graph of the solutions that are obtained.