基于上下解方法的p(x)-Kirchhoff型方程正解的存在性

The Existence of Positive Solutions for p(x)-Kirchhoff Type Equation Via Sub-supersolution Method

运用上下解方法和比较原则研究p(x)-Kirchhoff型方程组在Dirichlet边界条件下正解的存在性.首先,在定义域内构造适当的分段函数并验证该函数为问题的下解.其次,通过已有方程组的径向对称解找出该问题的上解.最后,根据比较原则得到该问题至少存在一个正解.

The existence of positive solutions of p(x)-Kirchhoff type equations under Dirichlet boundary conditions is studied by using the sub-super solution method and comparison principle.Firstly,an appropriate piecewise function is constructed in the definition domain and verified that the function is the subsolution of the problem.Secondly,the supersolution of the problem is found through the radial symmetric solution of the existing equations.Finally,according to the comparison principle,it is obtained that there is at least one positive solution of the problem.