The Existence Of Entire Radial Solutions For A Class Of （p₁,p₂）-Laplace Systems With Weighted Nonlinear Gradient Terms

We investigate the existence of increasing entire positive radial bounded and large solutions for a class of the(p1,p2)-Laplace systems (?) with weighted nonlinear gradient terms.The paper includes four parts.In the first part,we mainly introduce the significance of the topic and the research background.In the second part,we transform the existence of increasing entire positive radial solutions for a class of the(p1,p2)-Laplace system into an integral system by structuring an integral factor.Then,by using a truncation method,a monotone iterative method and Arzela-Ascoli theorem,we study the existence,the boundedness and the regularity of the increasing entire radial solutions to the(p1,p2)-Laplace systems when bi∈C[0,∞)are nonnegative,nontrivial functions;hi:[0,∞)→[0,∞)are increasing and continuous functions.Where,pi-1>qi≥>0(i=1,2),△piu=div(|▽u|pi-2▽u).The solutions are called entire radial solutions if u(|x|)=u(r),v(|x|)=v(r),r=|x|,x∈RN,u,v∈C1[0,∞)∩C2(0,∞).An entire solution(u,v)is called large solution if lim|x|→∞(x)=lim|x|→∞(x)=+∞.In the third part,we extend the results obtained in the second part to the more general(p1,p2)-Laplace system (?)where θi are nonnegative,nontrivial and continuous on RN,f1[0,∞)×[0,∞)→[0,∞),f2:[0,∞)→[0,∞)are increasing and continuous.We study the existence,the boundedness and the regularity of the increasing entire radial solutions for the above problem.In the fourth part,we summarize the full paper.