Note Of Global Solution For Three Classes Of Nonlinear Elliptic Equation (System)

In this paper, using a variational approach, we deal with a class of nonlinear elliptic systems derived from a potential and involving the p - Laplacian. Undersuitable assumptions on the nonlinearities, we show the existence in R^N of nontrivial solutions .Meanwhile by using fixed point principle, we obtain theexistence of infinitely many radial solutions for a class of p - Laplacian problemunder certain conditions. In addition, by using method of super-solution and sub-solution, we are concerned with existence, non-existence and the behavior at infinity of non-negative blow-up entire solutions of the class ofp - Laplacian problem in R^N.The main content of this paper is divided into three Chapters.In chapter two, we are concerned with a class of nonlinear elliptic systemsderived from a potential and involving the p - Laplacian.The nonlinearities on the right hand side are the gradient of a C¹-functional F and â–³_p is the so-called p-Laplacian operator i.e. A_p u=div(|â–½u|^p-2 â–½u),u and...