A Class Of Elliptic Systems In The Ring Domain Existence Of Positive Radial Solutions, Non-existence Of Multiple Solutions

Let be an annulus with boundary . In this paper we seek the positive radial solutions of the elliptic systemBy applying the change of variablescan be brought into the formIn our work, we show the existence, nonexistence and multiplicity of positive radial solutions for the system (1.5) and (1.6). By a fixed point theorem of cone expansion/compression type, we prove the following: THEOREM2.3.1: Assume either of the following cases hold:Then problem (1.5) has at least one positive radial solution.THEOREM2.3.2: Assume that there exist two distinct positive constants a, bsuch thatandThen problem (1.6) has at least one positive solution (u,v) such that between a and b whereTHEOREM2.3.3: Assume that there exists a positive constant c such that either of the following cases hold:Then problem (1.6) has at least two positive solutions (u1, v1). (u2,v2) such thatTHEOREM3.1.2: Assume that the following cases hold:Then problem (1.6) has at least two positive solutions (u1, v1). (u2. v2) such that where,andi = 1,2.