and Applied Analysis 3 that the partial derivatives fu and fv exist, the conjecture means that if for large |u| |v| the pair ( fu t, u, v ,−fv t, u, v ) 1.10 lies in a certain rectangle R α, β;a, b which does not intersect any of the eigenline Lk of LEVP 1.6 ; then BVP 1.1 is solvable. But they could not prove the conjecture. Recently, the present author 11 has partly answered this conjecture a...

In [4], the authors proved the uniqueness among the solutions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman-Kac formula proved in [4].

In [4], the authors proved the uniqueness among the solutions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman-Kac formula proved in [4].

We prove an existence and uniqueness result for ground states of one-dimensional Schrödinger-Newton equations.

We present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects ca...

In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in...

In this paper, we consider an inverse problem for three dimensional viscoelastic fluid flow equations, which arises from the motion of Kelvin-Voigt fluids in bounded domains (a hyperbolic type problem). This aims to reconstruct velocity and kernel memory term simultaneously, measurement described as integral over determination condition. By using contraction mapping principle appropriate space,...