Related papers: Schr\"odinger-Maxwell equations driven by mixed lo…
The paper considers the Schrodinger-Maxwell system with supercritical nonlinearitie. We prove the existence of at least one non-trivial weak solution. This result is already known for the subcritical case. In this paper, we extend it to the…
We present a new approach for search of coexisting classes of localised modes admitted by the repulsive (defocusing) scalar or vector nonlinear Schr\"odinger-type equations. The approach is based on the observation that generic solutions of…
We consider the focusing mass supercritical nonlinear Schr\"odinger equation with rotation \begin{equation*} iu_{t}=-\frac{1}{2}\Delta u+\frac{1}{2}V(x)u-|u|^{p-1}u+L_{\Omega}u,\quad (x,t)\in \mathbb{R}^{N}\times\mathbb{R}, \end{equation*}…
The nonlocal Darboux transformation for the stationary axially symmetric Schr\"odinger and Helmholtz equations is considered. Formulae for the nonlocal Darboux transformation are obtained and its relation to the generalized Moutard…
In this paper, we establish the existence of ground state solutions for a fractional Schr\"odinger equation in the presence of a harmonic trapping potential. We also address the orbital stability of standing waves. Additionally, we provide…
The present study is concerned with the following Schr\"{o}dinger-Poisson system involving critical nonlocal term $$ \left\{ \begin{array}{ll} -\Delta u+u-K(x)\phi |u|^3u=\lambda f(x)|u|^{q-2}u, & x\in\mathbb{R}^3, -\Delta \phi=K(x)|u|^5, &…
We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many standing…
We obtain weighted mixed inequalities for operators associated to a critical radius function. We consider Schr\"odinger Calder\'on-Zygmund operators of $(s,\delta)$ type, for $1<s\leq \infty$ and $0<\delta \leq 1$. We also give estimates of…
This work investigates radial solutions for nonlinear fractional Schr\"odinger equations driven by multiplicative noise. Leveraging radial deterministic and stochastic Strichartz estimates, we establish local well-posedness in the…
Multi-time wave functions are wave functions that have a time variable for every particle, such as $\phi(t_1,x_1,\ldots,t_N,x_N)$. They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in…
Many approximate solutions of the time-dependent Schr\"odinger equation can be formulated as exact solutions of a nonlinear Schr\"odinger equation with an effective Hamiltonian operator depending on the state of the system. We show that…
Complex Wadati-type potentials of the form $V(x)=-w^2(x) + iw_x(x)$, where $w(x)$ is a real-valued function, are known to possess a number of intriguing features, unusual for generic non-Hermitian potentials. In the present work, we…
In this paper, kinds of Schr\"{o}dinger type equations with slowly decaying linear potential and power type or convolution type nonlinearities are considered. By using the concentration compactness principle, the sharp Gagliardo-Nirenberg…
We study the existence of solutions for a class of nonlinear Schr\"odinger equations involving a magnetic field with mixed Dirichlet-Neumann boundary conditions. We use Lyusternik-Shnirelman category and the Morse theory to estimate the…
Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the…
In this paper, we are mainly concerned with the physically interesting static Schr\"{o}dinger-Hartree-Maxwell type equations \begin{equation*} (-\Delta)^{s}u(x)=\left(\frac{1}{|x|^{\sigma}}\ast |u|^{p}\right)u^{q}(x)…
We discuss the application of the Mountain Pass algorithm to the so-called quasi-linear Schrodinger equation, which is naturally associated with a class of nonsmooth functionals so that the classical algorithm is not directly applicable.
We study a nonlinear Schr\"odinger equation with logarithmic nonlinearity on a star graph $\mathcal{G}$. At the vertex an interaction occurs described by a boundary condition of delta type with strength $\alpha\in \mathbb{R}$. We…
In this paper we prove the existence of orbitally stable standing waves for the critical Schr\"{o}dinger operator, involving potential of the form $\left(\frac{N-2}{2}\right)^2|x|^{-2}$. The approach, being purely variational, is based on…
For the one-dimensional mass-critical/supercritical pseudo-relativistic nonlinear Schrodinger equation, a stationary solution can be constructed as an energy minimizer under an additional kinetic energy constraint and the set of energy…