Semilinear nonlocal elliptic equations with source term and measure data

Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations

We investigate quantitative properties of nonnegative solutions u(x) ≥ 0 to the semilinear diffusion equation Lu = f(u), posed in a bounded domain Ω ⊂ R with appropriate homogeneous Dirichlet or outer boundary conditions. The operator L may belong to a quite general class of linear operators that include the standard Laplacian, the two most common definitions of the fractional Laplacian (−∆) (0...

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

Nonlinear degenerate elliptic equations with measure data

In this paper we prove existence results for some nonlinear degenerate elliptic equations with data in the space of bounded Radon measures and we improve the results already obtained in Cirmi G.R., On the existence of solutions to non-linear degenerate elliptic equations with measure data, Ricerche Mat. 42 (1993), no. 2, 315–329.

Semilinear Nonlocal Differential Equations with Delay Terms

The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder’s fixed point theorem. We construct the fundamental solution, establish the Hölder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions ...

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. ...