具奇异非线性项p-Laplace方程Dirichlet问题解的存在唯一性

针对p-Laplace方程拟线性及非线性项在边界上的奇异特征,运用弱比较原理、上下解方法得到了该方程解的存在唯一性,证明了一类奇异拟线性方程边值问题的解的存在性和唯一性.通过研究该问题的逼近问题的解的存在性,得到了该问题的解存在且唯一,并且逼近问题的解收敛于该类问题的解.此外,还研究了一类奇异拟线性椭圆方程Dirichlet问题解的存在性,该类问题主要运用了上下解方法等得到了其解的存在性,并且通过证明其逼近问题解的存在性,得到了该类奇异拟线性椭圆方程Dirichlet问题解的存在性,所得到的解是弱解.

Existence and Uniqueness of Solutions for the p-Laplace Equation Dirichlet Problem with Singular Nonlinear Term

The feature of the p-Laplace equation is that the nonlinear term is singular and the equation is quasilinear.The comparison principle and the method of upper and lower solutions were used to inspect the existence and uniqueness of solutions of this equation.The existence and uniqueness of the solutions of a class of quasilinear equations boundary value problems with singular term were proved.Through the study of the existence of solutions of an approximation problem, it is shown that the solution exists and is unique, and the solutions of the approximation problem converge to the solution of such a problem.The existence of solutions of the quasilinear equation Dirichlet problems with singular nonlinear term was also discussed.The method of upper and lower solutions was mainly used to inspect the existence of its solution, and through the proof of its approximation problems, the existence of solutions of Dirichlet linear elliptic equations was proved.The obtained solution is a weak solution.