This thesis is devoted to the study of stochastic nonlinear Schrödinger equations (abbreviated as SNLS) with linear multiplicative noise in two aspects: the wellposedness in L(R), H(R) and the noise effects on blowup phenomena in the non-conservative case. 1. The well-posedness in L(R). The first fundamental question when dealing with SNLS is the well-posedness problem. In the first chapter, we...

In this article we investigate the existence of a solution to a semi-linear, elliptic, partial differential equation with distributional coefficients and data. The problem we consider is a generalization of the Lichnerowicz equation that one encounters in studying the constraint equations in general relativity. Our method for solving this problem consists of solving a net of regularized, semi-l...

The Horn-Schunck equations are a coupled system of two partial differential equations which aim at finding motion information in a given image sequence. Recent results [1, 2] asserted that this system is well-posed and can not be decoupled under any linear transformations. In this paper, two alternating iterative algorithms are proposed to solve this system. These algorithms have three properti...

The aim of this paper is to study the existence of solutions to a boundary value problem associated to a nonlinear fractional differential equation where the nonlinear term depends on a fractional derivative of lower order posed on the half-line. An appropriate compactness criterion and suitable Banach spaces are used and so a fixed point theorem is applied to obtain fixed points which are solu...

This paper deals with the existence of solutions for Riemann-Liouville fractional order boundary value problem infinite-point conditions posed on half-line via concept a family measures noncompactness in space functions C?,?(R+) satisfying H?lder condition and generalized Darbo fixed point theorem.

The classical Center-Focus problem posed by H. Poincaré in 1880’s asks about the characterization of planar polynomial vector fields such that all their integral trajectories are closed curves whose interiors contain a fixed point, a center. In this paper we describe a new general approach to the Center Problem.

The classical Center-Focus problem posed by H. Poincaré in 1880’s asks about the characterization of planar polynomial vector fields such that all their integral trajectories are closed curves whose interiors contain a fixed point (which is called a center). In this paper we describe a new general approach to the Center Problem.

The equilibrium problem defined by the Nikaidô–Isoda–Fan inequality contains a number of problems such as optimization, variational inequality, Kakutani fixed point, Nash equilibria, and others special cases. This paper presents picture for relationship between points Moreau proximal mapping solutions that satisfies some kinds monotonicity Lipschitz-type condition.