含有广义p-Laplacian算子的双曲型非线性微分方程的单调性方法

Monotonicity Method for Hyperbolic Type Nonlinear Differential Equation with Generalized p-Laplacian

利用伪单调算子和极大单调算子值域的扰动结果,得到了含有广义p-Laplacian算子、具混合边值条件的双曲型非线性微分方程存在唯一解的抽象结论,是对含有广义p-Laplaucian算子的非线性椭圆方程和抛物方程相关研究工作的推广.运用了一些新的证明技巧.而且,展示了这个唯一解与某极大单调算子零点之间的关系.

By using the results on the perturbations of the ranges for pseudo-monotone operators and maximal monotone operators,we present the abstract result for the existence of the unique solution of hyperbolic type nonlinear differential equation involving the generalized p-Laplacian with mixed boundaries.It is an extension of the corresponding studies on nonlinear elliptic equation and nonlinear parabolic equation with generalized p-Laplacian.Some new techniques are employed in the discussion.Moreover,the connections between the unique solution studied in this paper and the zero point of a maximal monotone operator is exemplified.