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This paper deals with a Cauchy problem for the Helmholtz equa- tion in multiple dimensions.We want to obtain the solution u on the boundary z = 0 from the given function g ontheside z = 1. This proble...
In this paper, we consider in R^n the Cauchy problem for nonlinear Schrodinger equation with initial data in Sobolev space W^{s,p} for p<2. It is well known that this problem is ill posed. However, We...
Abstract: In the present paper we are concerned with the Novikov--Veselov equation at negative energy, i.e. with the $(2 + 1)$--dimensional analog of the KdV equation integrable by the method of inver...
In this paper, we study the Cauchy problem of a two-component b-family equation. We first establish the local well-posedness for a two-component b-family equation by Kato’s semigroup theory. Then, we ...
We consider the Cauchy problem for (energy-subcritical) nonlinear Schr¨odinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a wel...
We consider the Cauchy problem for the nonlinear Schr¨odinger equation i@tu + u = 1u + 2|u| u in RN, in Hs subcritical case 0  < 4 N−2s , when 0 < s < N 2 and 0  < +1, when s > N 2 . We...
This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing antiplane shear motions in nonlocal elasticity.

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