Green-Rvachev's quasi-function method for constructing two-sided approximations to positive solution of nonlinear boundary value problems
Keywords: positive solution, semilinear elliptic boundary value problem, heterotone operator, two-sided approach, Green-Rvachev's quasi-function
Published online: 2018-12-31
A homogeneous Dirichlet problem for a semilinear elliptic equations with the Laplace operator and Helmholtz operator is investigated. To construct the two-sided approximations to a positive solution of this boundary value problem the transition to an equivalent nonlinear integral equation (with the help of the Green-Rvachev's quasi-function) with its subsequent analysis by methods of the theory of semi-ordered spaces is used. The work and efficiency of the developed method are demonstrated by a computational experiment for a test problem with exponential nonlinearity.