Some Second Order Elliptic Partial Differential Equations On Unbounded Domain

This thesis contains three chapters In the second chapter, we consider a noncooperative system of p-Laplacian elliptic equationsApplying Principle of Symmetric Criticality and a Limit Index Theory, under some assumptions on Fu, Fv, we can obtain the existence of infinitely many radial solutions and nonradial solutions for the above system, which extends some results in [30] In the third chapter, we consider the semilinear elliptic equationUnder certain hypotheses on V and f, we obtain the existence of infinitely many radial solutions and nonradial solutions for the above equation, which extends some results in [6]In the fourth chapter, we formulate a concentration-compactness principle at infinity which extends a result introduced by J Chabrowski [11] Then we consider some quasilinear elliptic equations in some classes of unbounded domains by solving their corresponding constrained minimization problems under certain conditions We show the existence of positive solutions of those equations via the concentration-compactness principle at infinity, which extends some results in [23]...