A Computational Procedure to Find Positive Numerical Solutions of a Boundary Value Problem with Nonlinear Terms
Abstract
In this work we present a numerical approach for finding positive solutions of the type −Δu = λf(u) for x ∈ Ω, with Dirichlet boundary condition, where f is a superlinear function of u. We will show in which range of λ, this problem achieves multiple numerical solutions and what is the behavior of the branches of solutions.
Keywords
Elliptic boundary value problems, multiple solutions, finite difference method
