【摘要】 本文考虑如下非线性发展方程组的初边值问题u″+ Au -△ u′-α| v|ρ+ 2 | u|ρu =0 ,　 v″+ Av -△ v′-α| u|ρ+ 2 | v|ρv =0 ,其中 A为 p-Laplace算子 ,α∈ R,ρ>-1均为常数 ,证明了整体解的存在性及渐近性 ,得到了当初始能量为正但有上界时解的爆破性条件更多还原

【Abstract】 This paper consider the following initial boundary value problemu″+Au-△u′-α|v| ρ+2|u| ρu=0, v″+Av-△v′-α|u| ρ+2|v| ρv=0,where A is the p-Laplace operator, α∈R, ρ>-1 are constant. We prove the existence of the global solution when initial data belongs to potential well and get the blow-up of the solution when the initial energry is positive, but appropriately bounded.更多还原