In this article, an optimal control problem subject to a semilinear elliptic equation and mixed control-state constraints is investigated. The problem data depends on certain parameters. Under an assumption of seperation of the active sets and a second-order sufficient optimality condition, Bouliganddifferentiability (B-differentiability) of the solutions with respect to the parameter is establ...

In this note we are mainly concerned with existence result for semilinear semipositone elliptic equation of the form ⎧⎨ ⎩ −Δu = λa(x)vα − c, x ∈ Ω, −Δv = λb(x)uβ − c, x ∈ Ω, u = v = 0, x ∈ ∂Ω, where Δ denote the Laplacian operator, Ω is a bounded domain in RN (N > 1) with ∂Ω of class C2, λ, c are positive parameters, α, β > 0 and the weight a(x), b(x) satisfying a(x) ∈ C(Ω), b(x) ∈ C(Ω) and a(x...

By means of a penalization scheme due to del Pino and Felmer, we prove the existence of single–peaked solutions for a class of singularly perturbed quasilinear elliptic equations associated with functionals which lack of smoothness. We don’t require neither uniqueness assumptions on the limiting autonomous equation nor monotonicity conditions on the nonlinearity. Compared with the semilinear ca...

We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffusegray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local op...

This paper is concerned with the derivation and analysis of first-order necessary optimality conditions for a class multiobjective optimal control problems governed by an elliptic non-smooth semilinear partial differential equation. Using adjoint calculus inverse non-linear non-differentiable directional derivative solution map considered PDE, we extend concept strong stationarity to setting de...

We consider an inverse problem regarding the detection of small conductivity inhomogeneities in a boundary value for semilinear elliptic equation. For such problem, that is related to cardiac electrophysiology, asymptotic expansion potential due presence was established [4]. Starting from this we derive Lipschitz continuous ...

In this article, an optimal control problem subject to a semilinear elliptic equation and mixed control-state constraints is investigated. The problem data depends on certain parameters. Under an assumption of seperation of the active sets and a second-order sufficient optimality condition, Bouliganddifferentiability (B-differentiability) of the solutions with respect to the parameter is establ...

On a bounded smooth domain Ω ⊂ R we study solutions of a semilinear elliptic equation with an exponential nonlinearity and a Hardy potential depending on the distance to ∂Ω. We derive global a priori bounds of the Keller–Osserman type. Using a Phragmen–Lindelöf alternative for generalized sub and super-harmonic functions we discuss existence, nonexistence and uniqueness of so-called large solut...