Semilinear elliptic systems with measure data

Existence and stability of solutions of general semilinear elliptic equations with measure data

Monotone Iterative Technique for Semilinear Elliptic Systems

We develop monotone iterative technique for a system of semilinear elliptic boundary value problems when the forcing function is the sum of Caratheodory functions which are nondecreasing and nonincreasing, respectively. The splitting of the forcing function leads to four different types of coupled weak upper and lower solutions. In this paper, relative to two of these coupled upper and lower so...

Locating the peaks of semilinear elliptic systems

We consider a system of weakly coupled singularly perturbed semilinear elliptic equations. First, we obtain a Lipschitz regularity result for the associated ground energy function Σ as well as representation formulas for the left and the right derivatives. Then, we show that the concentration points of the solutions locate close to the critical points of Σ in the sense of subdifferential calcul...

Optimal Control of Semilinear Elliptic Equations in Measure Spaces

Optimal control problems in measure spaces governed by semilinear elliptic equations are considered. First order optimality conditions are derived and structural properties of their solutions, in particular sparsity, are discussed. Necessary and sufficient second order optimality conditions are obtained as well. On the basis of the sufficient conditions, stability of the solutions is analyzed. ...

Semilinear Elliptic Systems With Exponential Nonlinearities in Two Dimensions ∗

We establish a priori bounds for positive solutions of semilinear elliptic systems of the form 8><>>>: −∆u = g(x, v) , in Ω −∆v = f(x, u) , in Ω u > 0 , v > 0 in Ω