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Stationary problem related to the nonlinear Schrödinger equation on the unit ball
In this paper, we study the stability of standing waves for the nonlinear Schrodinger equation on the unit ball in with Dirichlet boundary condition. We generalize the result of Fibich and Merle
Existence of a ground state and scattering for a nonlinear Schrödinger equation with critical growth
We study the energy-critical focusing nonlinear Schrödinger equation with an energy-subcritical perturbation. We show the existence of a ground state in the four or higher dimensions. Moreover, we
Existence of a ground state and blow-up problem for a nonlinear Schrodinger equation with critical growth
In this paper we show the existence of ground-state solutions for the energy-critical NLS perturbed with subcritical terms when the space dimension $d\geq4$. However in dimension three, we show that
A bifurcation diagram of solutions to an elliptic equation with exponential nonlinearity in higher dimensions
We consider the following semilinear elliptic equation: where B 1 is the unit ball in ℝ d , d ≥ 3, λ > 0 and p > 0. Firstly, following Merle and Peletier, we show that there exists an eigenvalue λ
Existence and uniqueness of singular solution to stationary schrodinger equation with supercritical nonlinearity
In this paper, we study a singular solution to the following elliptic equations: \begin{equation*} \left\{\begin{array}{ll} - \Delta u + |x|^{2}u - \lambda u - |u|^{p-1}u = 0, \quad x \in
Existence and Stability of Standing Waves For Schrödinger-Poisson-Slater Equation
Abstract We study the existence and stability of standing wave for the Schrödinger-Poisson-Slater equation in three dimensional space. Let p be the exponent of the nonlinear term. Then we first show
Instability of standing waves for the Klein-Gordon-Schrödinger system
We study the orbital instability of standing wave solutions for the Klein-Gordon-Schrodinger system in three space dimensions. It is proved that the standing wave is unstable if the frequency is
Linear instability and nondegeneracy of ground state for combined power-type nonlinear scalar field equations with the Sobolev critical exponent and large frequency parameter
Abstract We consider combined power-type nonlinear scalar field equations with the Sobolev critical exponent. In [3], it was shown that if the frequency parameter is sufficiently small, then the
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