含有广义p-Laplace算子的抛物边值问题解的存在性

Existence of Solution to Parabolic Boundary Value Problem with Generalized p-Laplacian Operator

利用极大单调单调算子值域的扰动结论,借助于构造辅助方程的技巧,研究了一类含有广义p-Laplace算子且具有混合边值条件的非线性抛物方程,并得到了这类非线性边值问题解的存在性的抽象结论.文中所用方法是对以往工作的推广和补充.

By using a perturbation result on the ranges of maximal monotone operators,and by using a method of constructing an auxiliary nonlinear equation,a nonlinear parabolic equation involving the generalized p-Laplacian operator with mixed boundary conditions is studied in this paper.An abstract result of the existence of solution for this nonlinear boundary value problem is obtained.The method used in this paper extends and complements some of the previous work.