CAJ | 학술논문

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。
침대 p-Laplace 방정의선성급비선성항재변계상적기이특정，운용약비교원리、상하해방법득도료해방정해적존재유일성，증명료일류기이의선성방정변치문제적해적존재성화유일성。통과연구해문제적핍근문제적해적존재성，득도료해문제적해존재차유일，병차핍근문제적해수렴우해류문제적해。차외，환연구료일류기이의선성타원방정 Dirichlet 문제해적존재성，해류문제주요운용료상하해방법등득도료기해적존재성，병차통과증명기핍근문제해적존재성，득도료해류기이의선성타원방정 Dirichlet 문제해적존재성，소득도적해시약해。
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.