摘要
主要考察一类带有Dirichlet边界条件的p-Laplace非线性椭圆型方程组正解的存在性.由于所考察的p-Laplace方程组具有对称性.首先,利用山路引理求解相应方程的形式解,并验证了解的正性,进而得到原方程组正的上解;其次,在所构造的方程组上下解区间上,通过解耦系统构造合适的映射,最终利用Leray-Schauder不动点定理,得到p-Laplace方程组正解的存在性.
The existence of positive solutions to p-Laplace nonlinear elliptic system with Dirichlet boundary conditions is investigated.First,with the symmetry of the p-Laplace system and Mountain Pass Theorem,the form solution to the corresponding single equation of the original system is obtained and its positiveness is proved.The positive sup-solution to the original system is obtained.Second,the appropriate mapping is structured with the solution to decoupled system in the intervals of sub-super solutions.Finally,with the Leray-Schauder's fixed point theorem,the existence of positive solutions is obtained.
出处
《河北北方学院学报(自然科学版)》
2010年第2期6-10,共5页
Journal of Hebei North University:Natural Science Edition
基金
河南省教育厅项目(2009B110009)
河南理工大学研究生学位论文创新基金(2008-M-29)