相关论文: On the behavior of solutions to Schr\"odinger equa…

Asymptotics of solutions to Schroedinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis-Kato type procedure, we…

The asymptotic behavior of solutions to Schr\"odinger equations with singular homogeneous potentials is investigated. Through an Almgren type monotonicity formula and separation of variables, we describe the exact asymptotics near the…

This paper deals with a class of nonlinear elliptic equations involving a critical power-nonlinearity as well as a potential featuring multiple inverse square singularities. When the poles form a symmetric structure, it is natural we wonder…

We study the asymptotic behaviour of solutions to semi-classical nonlinear Schrodinger equations with a potential, for concentrating and oscillating initial data, when the nonlinearity is repulsive and the potential is a polynomial of…

In this paper we study the asymptotic behavior of solutions to an elliptic equation near the singularity of an inverse square potential with a coefficient related to the best constant for the Hardy inequality. Due to the presence of a…

We study positive bound states for the semiclassical stationary nonlinear Schr\"odinger equation. We are especially interested in solutions which concentrate on a lower dimensional sphere. We adopt a purely variational approach which allows…

The asymptotic iteration method is used to find exact and approximate solutions of Schroedinger's equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent).…

We study positivity, localization of binding and essential self-adjointness properties of a class of Schroedinger operators with many anisotropic inverse square singularities, including the case of multiple dipole potentials.

In this study, we examine the asymptotic behavior of solutions to nonlinear Schr\"{o}dinger equations with time-dependent harmonic oscillators and prove the time-decay property of solutions in the case of a long range power type…

In this work we shall review some of our recent results concerning unique continuation properties of solutions of Schr\"odinger equations. In this equations we include linear ones with a time depending potential and semi-linear ones.

We propose in this paper to study the solutions of some nonlinear elliptic equations with singular potential.

This paper is devoted to the study of the large-time asymptotics of the small solutions to the matrix nonlinear Schr\"{o}dinger equation with a potential on the half-line and with general selfadjoint boundary condition, and on the line with…

A class of nonlinear Schroedinger equations with critical power-nonlinearities and potentials exhibiting multiple anisotropic inverse square singularities is investigated. Conditions on strength, location, and orientation of singularities…

In this paper, we study asymptotic behavior of solution near 0 for a class of elliptic problem. The uniqueness of singular solution is established

We investigate uniqueness of solutions to certain classes of elliptic and parabolic equations posed on metric graphs. In particular, we address the linear Schr\"odinger equation with a potential, and the heat equation with a variable…

In this paper, we prove a sharp uniqueness result for the singular Schr\"odinger equation with an inverse square potential. This will be done without assuming geometrical restrictions on the observation region. The proof relies on a recent…

We study the existence and concentration of positive and nodal solutions to a Schr\"odinger equation in the presence of a shrinking self-focusing core of arbitrary shape. Via a suitable rescaling, the concentration gives rise to a limiting…

We consider the semilinear electromagnetic Schr\"{o}dinger equation (-i\nabla+A(x))^{2}u + V(x)u = |u|^{2^{\ast}-2}u, u\in D_{A,0}^{1,2}(\Omega,\mathbb{C}), where $\Omega=(\mathbb{R}^{m}\smallsetminus{0})\times\mathbb{R}^{N-m}$ with $2\leq…

We investigate the uniqueness, in suitable weighted $\ell^p$ spaces, of solutions to the Schr\"odinger equation with a potential, posed on infinite graphs. The potential can tend to zero at infinite with a certain rate.

We investigate numerically by a conservative difference scheme in complex arithmetic the head-on and takeover collision dynamics of the solitary waves as solutions of linearly Coupled Nonlinear Schr\"odinger Equations for various initial…