四阶p-Laplace方程组边值问题的正解

Positive solutions of fourth order p-Laplacian boundary value problems

研究如下非线性p-Laplace方程组边值问题的正解的存在性{(︱u″︱^(p-1) u″)″=f(t,u,v),t∈(0,1)(︱v″︱^(p-1) v″)″=g(t,u,v),t∈(0,1)u(0)=u(1)=u″(0)=u″(1)=0,v(0)=v(1)=v″(0)=v″(1)=0其中p>0,q>0,f∈C([0,1]×R_+~2,R+),g∈C([0,1]×R_+~2,R+).利用不动点指数理论和先验估计方法,得到了该问题正解的存在性结果.

This paper deals with the existence of positive solutions for the system of p-Laplacian boundary value problems {(︱u″︱^(p-1) u″)″=f(t,u,v),t∈(0,1)(︱v″︱^(p-1) v″)″=g(t,u,v),t∈(0,1)u(0)=u(1)=u″(0)=u″(1)=0,v(0)=v(1)=v″(0)=v″(1)=0 where p>0,q>0,f∈C([0,1]×R_+~2,R+),g∈C([0,1]×R_+~2,R+).By using fixed-point index theory combined with a priori estimates,it establishes the existence of positive solutions for the problem results.