The objective of this paper is to investigate the existence mild solutions and optimal controls for a class fractional neutral stochastic integrodifferential equations driven by Rosenblatt process Poisson jumps in Hilbert spaces. First we establish new set sufficient conditions aforementioned systems using successive approximation approach. results are formulated proved calculus, solution opera...

In dimension two, we investigate a free energy and the ground state of Schrödinger–Poisson system coupled with logarithmic nonlinearity in terms underlying functional inequalities which take into account scaling invariances problem. Such can be considered as nonlinear Schrödinger equation cubic but nonlocal Poisson nonlinearity, local nonlinearity. Both cases repulsive attractive forces are con...

The qualitative theory for planar dynamical systems is used to study the bifurcation of wave solutions space-fractional nonlinear Schrödinger equation with multiplicative white noise. Employing first integral, we introduce some new solutions, assorted into periodic, solitary, and kink solutions. dependence on initial conditions investigated. Some are clarified by display their 2D 3D representat...

Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schrödinger equation for single-particle orbitals. Due to nonlinearity and complexity this set of equations, one believes in the iterative method for the solution that should consist in consecutive improvement of the potential and the electron density u...