Stability of nonlinear elliptic systems with distributed parameters and variable boundary data

Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian

“…We extend our considerations to cover also the case of the nonlocal, fractional Laplace operator being the infinitesimal generator of Lévy processes; see, for instance, [ 4 – 7 ], allowing, contrary to the continuous Brownian motion, for jumps. We prove the analogous stability results as for the Brownian motion with the Laplace operator involved obtained in [ 1 – 3 ].…”

“…The equation under consideration is the generalization of the nonlinear Poisson equation involving the Brownian diffusion expressed by the local Laplace operator fully analyzed in [ 1 – 3 ]. We extend our considerations to cover also the case of the nonlocal, fractional Laplace operator being the infinitesimal generator of Lévy processes; see, for instance, [ 4 – 7 ], allowing, contrary to the continuous Brownian motion, for jumps.…”

Dynamical system modeling fermionic limit

“…Moreover, we choose some special family of the solutions characterized by the limit at minus infinity, not the whole set of possible solutions. The continuous dependence on parameters of the whole set of solutions for elliptic equations was established among others in [4,5,6,7]. One should point out that the passage to the singular limit was rigorously verified both for the related Navier-Stokes-Fourier-Poisson system by Laurençot and Feireisl in [15] while Golse and Saint-Raymond in [18] dealt with celebrated Navier-Stokes and Boltzmann equations.…”

“…The functional is coercive and can be decomposed into compact and continuous part and lower-semicontinuous and convex part thus making the direct approach feasible to yield the existence of minimizer. It seems that the results of [4,5,6,7] can be used to get the continuity of the set of minimizers at least for sufficiently small mass M > 0. The only obstacle is that the limiting functional is defined over the space of ρ log ρ integrable functions as η → 0 + .…”

Lagrange problem for fractional ordinary elliptic system via Dubovitskii–Milyutin method

“…also [17]). http://www.journals.vu.lt/nonlinear-analysis Existence of optimal solutions and stability results concerning the case of β = 1 can be found in [5,6,23]. Necessary first-order optimality conditions for β = 1 can be deduced in some cases from the results obtained in [12] and [13].…”