具有对流项的(2,p)-Laplace方程非负解的存在性

Existence of non-negative solution for(2,p)-Laplace equation with convection term

在非线性项f满足适当的限制性条件下,研究具有对流项的(2,p)-Laplace方程非负解的存在性。根据非线性项f的限制性条件,得到了Nemytskii算子的连续性和有界性;利用(2,p)-Laplace算子的性质以及Sobolev紧嵌入定理,将方程转化为一个不动点问题;利用锥理论和不动点指数理论解决不动点问题,得到了方程非负解的存在性。

Under appropriate restrictive conditions on the nonlinear term f,the existence of non-negative solution for(2,p)-Laplace equation with convection term were considered.According to the restrictive conditions on the nonlinear term f,the continuity and boundedness of Nemytskii operator are obtained;Using the properties of(2,p)-Laplace operator and Sobolev compact embedding theorem,the equation is transformed into a fixed point problem.Using the cone theory and fixed point index theory to solve the fixed point problem,the existence of non-negative solution of the equation is obtained.