广义Baouendi-Grushin向量场上具有奇异位势的半线性退化发展不等方程

Semilinear Degenerate Evolution Inequalities with Singular Potential on Generalized Baouendi-Grushin Vector Fields

研究与广义Baouendi-Grushin算子相关的具有奇异位势退化发展不等方程整解的存在性和不存在性,推广了文献中的结果.解的存在性定理的证明基于上解方法和变形Bessel函数的运用,解的不存在性定理则根据试验函数方法得到.

The purpose of this paper is to study the existence and nonexistence of global solutions to the degenerate evolution inequalities with singular potential correlated to the generalized Baouendi-Grushin operator. The obtained results extend and improve upon those in the literature. To prove the existence results, we used the method of supersolution and the modified Bessel function. The nonexistence results are established by means of the test function method.