In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely obstacle problem. Since adopt a numerical point of view, first relax feasible domain problem, then using both mathematical programming methods penalization get optimality conditions with smooth Lagrange multipliers. Some experimen...

We study the well posedness of nonlinear Schrödinger (NLS) equation with a point interaction and power nonlinearity in dimension two three. Behind autonomous interest problem, this is model evolution so called singular solutions that are known analysis semilinear elliptic equations. show Cauchy problem for NLS considered enjoys local existence uniqueness strong (operator domain) solutions, depe...

Given a conformally transversally anisotropic manifold (M, g), we consider the semilinear elliptic equation $$\begin{aligned} (-\Delta _{g}+V)u+qu^2=0\quad \hbox { on}\ M. \end{aligned}$$ We show that an priori unknown smooth function q can be uniquely determined from knowledge of Dirichlet-to-Neumann map associated to equation. This extends previously known results works Feizmohammadi and Oksa...