Nonlinear elliptic equations with measure valued absorption potentials

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.

Measure boundary value problems for semilinear elliptic equations with critical Hardy potentials

Article history: Received 16 October 2014 Accepted after revision 26 January 2015 Available online 26 February 2015 Presented by Haïm Brézis Let Ω ⊂ RN be a bounded C2 domain and Lκ = − − κ d2 where d = dist(., ∂Ω) and 0 < κ ≤ 4 . Let α± = 1 ± √ 1− 4κ , λκ the first eigenvalue of Lκ with corresponding positive eigenfunction φκ . If g is a continuous nondecreasing function satisfying ∫ ∞ 1 (g(s)...

Nonlinear Elliptic Equations with Fractional Diffusion

Non-linear elliptic systems with measure-valued right hand side

We prove existence of a solution u for the nonlinear elliptic system -div a(x,u,Du) =/ i in V(Q,), u = 0 on dfl where \x is Radon measure on Q with finite mass. In particular we show that if the coercivity rate of a lies in the range (1,2 — ^] then u is approximately differentiable and the equation holds with Du replaced by ap Du. The proof relies on an approximation of // by smooth functions f...

Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.