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We prove a nonlinear Poisson type formula for the Schrodinger group. Such a formula had been derived in a previous paper by the authors, as a consequence of the study of the asymptotic behavior of nonlinear wave operators for small data. In this note, we propose a direct proof, and extend the range allowed for the power of the nonlinearity to the set of all short range nonlinearities. Moreover, energy-critical nonlinearities are allowed.
This paper is devoted to study the existence and multiplicity solutions for the nonlinear Schrodinger-Poisson systems involving fractional Laplacian operator: begin{equation}label{eq*} left{ aligned &(-Delta)^{s} u+V(x)u+ phi u=f(x,u), quad &te
We consider a system of two coupled ordinary differential equations which appears as an envelope equation in Bose-Einstein Condensation. This system can be viewed as a nonlinear extension of the celebrated model introduced by Landau and Zener. We sho
We study the wave equation in the exterior of a bounded domain $K$ with dissipative boundary condition $partial_{ u} u - gamma(x) u = 0$ on the boundary $Gamma$ and $gamma(x) > 0.$ The solutions are described by a contraction semigroup $V(t) = e^{tG}
We consider the Schrodinger equation with nonlinear dissipation begin{equation*} i partial _t u +Delta u=lambda|u|^{alpha}u end{equation*} in ${mathbb R}^N $, $Ngeq1$, where $lambdain {mathbb C} $ with $Imlambda<0$. Assuming $frac {2} {N+2}<alpha<fra
In this thesis we consider a magnetic Schrodinger inverse problem over a compact domain contained in an infinite cylindrical manifold. We show that, under certain conditions on the electromagnetic potentials, we can recover the magnetic field from bo