An ∞-dimensional inhomogeneous Langevin's equation

Inverse Problem for an Inhomogeneous Schrödinger Equation * †

Let (− k 2)u = −u + q(x)u − k 2 u = δ(x), x ∈ R, ∂u ∂|x| − iku → 0, |x| → ∞. Assume that the potential q(x) is real-valued and compactly supported: q(x) = q(x), q(x) = 0 for |x| ≥ 1, 1 −1 |q|dx < ∞, and that q(x) produces no bound states. Let u(−1, k) and u(1, k) ∀k > 0 be the data. Theorem.Under the above assumptions these data determine q(x) uniquely.

Inhomogeneous infinity Laplace equation ✩

We present the theory of the viscosity solutions of the inhomogeneous infinity Laplace equation ∂xi u∂xj u∂ 2 xixj u = f in domains in Rn. We show existence and uniqueness of a viscosity solution of the Dirichlet problem under the intrinsic condition f does not change its sign. We also discover a characteristic property, which we call the comparison with standard functions property, of the visc...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Multiple solutions for an inhomogeneous semilinear elliptic equation in R

In this paper, we will investigate the existence of multiple solutions for the general inhomogeneous elliptic problem   − u+ u = f (x, u) + μh (x) , x ∈ R , u ∈ H (RN) , (1.1)μ where h ∈ H−1 (RN), N ≥ 2, |f (x, u)| ≤ C1up−1 + C2u with C1 > 0, C2 ∈ [0, 1) being some constants and 2 < p < +∞. ∗Research supported in part by the Natural Science Foundation of China and NSEC †Research supported ...

Transport in an inhomogeneous interacting one-dimensional system.

Transport through a one–dimensional wire of interacting electrons connected to semi–infinite leads is investigated using a bosonization approach. An incident electron is transmitted as a sequence of partial charges. The dc conduc-tance is found to be entirely determined by the properties of the leads. The dynamic nonlocal conductivity is rigorously expressed in terms of the transmission. For ab...