Sharif Digital Repository

This thesis is devoted to prove the existance of solution and structure of solu­ tion for some partial differential equations by using some modern topological and variational thechniques. Taking direction from the literature, this thesis is interested in existence, uniqueness, blow-up in finite time for some evolution equations, multiplicity and radial solution for certain elliptic partial differential equations.-Employing Fibrering, Galerkins, Mountain Pass-Lemma and lions com­ pactness Lemma are sharp in this thesis to prove the exsistence and multiplicity of solutions and overcome lack of compactness in some cases  

Matrix completion is an emerging field that is proposed after new and attractive field of compressed sensing. Matrix completion is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. In general, accurate recovery of a matrix from a small number of entries is impossible, but the knowledge that the unknown matrix has low rank radically changes this premise, making the search for solutions meaningful. Matrix completion problem comes up in great number of applications,including collaborative filtering, machine learning, control, image processing, sensor networks, system identification and communications (spectrum sensing and network coding). In this...