含超临界指数的p&q-拉普拉斯方程的多重解

证明了如下含超临界指数的pq-拉普拉斯方程-△_pu-△_qu+|u|~(r-2)u=γ|u|~(s-2)u,x∈Ω,u=0,x∈Ω,满足一定假设下,存在无穷多弱解.     

MULTIPLE POSITIVE SOLUTIONS TO A CLASS OF MODIFIED NONLINEAR SCHR?DINGER EQUATION IN A HIGH DIMENSION

The existence and multiplicity of positive solutions for equation(1.1) with the new critical exponent 4

* shall be investigated in a high dimension.The conclusions extend the relative results recently attained in [1] for the one-dimensional case.More precisely,as the coefficient a(x) in the nonlinearity is sign-changing,the modified term 2(Δ(|u|²))u is still helpful for obtaining multiple positive solutions in a high dimension,even if a sign condition like■(als...