相关论文: On the Schrodinger-Maxwell equations under the eff…
A nonlocal-in-time problem for the abstract Schr\"odinger equation is considered. By exploiting the linear nature of nonlocal condition we derive an exact representation of the solution operator under assumptions that the spectrum of…
We present analytical results and numerical simulations for a class of nonlinear dispersive equations in two spatial dimensions. These equations are of (derivative) nonlinear Schr\"odinger type and have recently been obtained in \cite{DLS}…
This paper is devoted to a comprehensive study of the nonlinear Schr\"odinger equations with combined nonlinearities of the power-type and Hartree-type in any dimension n\ge3. With some structural conditions, a nearly whole picture of the…
We establish the existence of an entire solution for a class of stationary Schr\"{o}dinger equations with subcritical discontinuous nonlinearity and lower bounded potential that blows-up at infinity. The abstract framework is related to…
We prove the unconditional uniqueness of solutions to the derivative nonlinear Schr\"odinger equation (DNLS) in an almost end-point regularity. To this purpose, we employ the normal form method and we transform (a gauge-equivalent) DNLS…
The paper offers the method of discovering of some class of solutions for the nonlinear Schroedinger equation. An algorithm of constructive solving of the Cauchy periodic problem with a finite-gap initial condition was also obtained.
We present new solutions in terms of elementary functions of the multi-component nonlinear Schr\"odinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton, breather, dromion and lump solutions. These…
We study the solution theory of the nonlinear Schr\"odinger equation with a concentrated nonlinearity on the torus. In particular, we establish existence and uniqueness of global energy-conserving solutions for initial data in $H^1$. Our…
We prove the existence of infinitely many solutions $\lambda_1, \lambda_2 \in \mathbb{R}$, $u,v \in H^1(\mathbb{R}^3)$, for the nonlinear Schr\"odinger system \[ \begin{cases} -\Delta u - \lambda_1 u = \mu u^3+ \beta u v^2 & \text{in…
We prove global well-posedness for the cubic nonlinear Schr\"odinger equation with nonlinearity concentrated on a homogeneous Poisson process.
We consider an elliptic system of Schr\"odinger-Bopp-Podolsky type in a bounded and smooth domain of R3 with a non constant coupling factor. This kind of system has been introduced in the mathematical literature in [14] and in the last…
Based on some ideas introduced by Benci and Cerami \cite{benci-cerami_calvar}, we obtain an abstract result that establishes a version of the Morse relations. Afterward, we use this result to prove multiplicity of solutions for a nonlinear…
We consider the question of global existence of small, smooth, and localized solutions of a certain fractional semilinear cubic NLS in one dimension, $$i\partial_t u - \Lambda u = c_0{|u|}^2 u + c_1 u^3 + c_2 u \bar{u}^2 + c_3 \bar{u}^3,…
We look for positive solutions to the nonlinear Schrodinger equation with a potential, under the hypothesis of zero mass on the nonlinearity, in a particular situation. Existence and multiplicity results are provided.
In this paper we study a system which is equivalent to a nonlocal version of the well known Brezis Nirenberg problem. The difficulties related with the lack of compactness are here emphasized by the nonlocal nature of the critical nonlinear…
We consider a semilinear elliptic problem with a nonlinear term which is the product of a power and the Riesz potential of a power. This family of equations includes the Choquard or nonlinear Schroedinger--Newton equation. We show that for…
We prove the existence of a ground state and infinitely many geometrically distinct solutions for static nonlinear Maxwell's equations on $\mathbb{R}^3$. Our existence result relies on a variant of the Symmetric Mountain Pass Theorem that…
A class of discrete nonlinear Schrodinger equations with arbitrarily high order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the…
It is proved that the KAM tori (thus quasi-periodic solutions) are long time stable for nonlinear Schrodinger equation.
This is the first part of a two-paper series studying nonlinear Schr\"odinger equations with quasi-periodic initial data. In this paper, we consider the standard nonlinear Schr\"odinger equation. Under the assumption that the Fourier…