By means of a Picone’s type identity, we prove uniqueness and oscillation of solutions to an elliptic semilinear equation with Dirichlet boundary conditions.

We consider a pointwise tracking optimal control problem for semilinear elliptic partial differential equation. derive the existence of solutions and analyze first and, necessary sufficient, second order optimality conditions. devise two strategies discretization to approximate solution problem: semidiscrete scheme where variable is not discretized---the so-called variational approach---and ful...

In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order semilinear elliptic equations. We first introduce several approximate dual problems, and briefly discuss the target problem class. We then review some standard facts concerning conforming finite element discretization and error-estimate-driven adaptive finite element me...