On the initial value problem for a nonlinear Schro¨dinger equation

On the Derivation of the Time-Dependent Equation of Schro dinger

for some quantum system S it is usually pointed out that time is a parameter, not enjoying the status of a quantum operator. However, it is almost never pointed out that the time occurring in HS(t) always is a classical time arising from the classical time development (according to Newton or Maxwell equations) of external fields or material particles interacting with the quantum system. In this...

Initial Value Problem for the Wave Equation

Nonhomeomorphic compact Hausdorff spaces X and Y and an isomorphism : C(X) -> C(Y) (onto) are constructed such that ||c/>|| \4>~ || = 2. Amir had asked if such a d> exists with || \\ ||cf> || < 3.

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

The Initial-boundary Value Problem for the 1d Nonlinear Schrödinger Equation on the Half-line

We prove, by adapting the method of Colliander-Kenig [9], local wellposedness of the initial-boundary value problem for the one-dimensional nonlinear Schrödinger equation i∂tu+∂ 2 x u+λu|u|α−1 = 0 on the half-line under low boundary regularity assumptions.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation