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| 带扰动参数的拟线性椭圆方程正解的存在性 | |
| 引用本文： | 孔丽华,沈自飞. 带扰动参数的拟线性椭圆方程正解的存在性[J]. 浙江师范大学学报(自然科学版), 2012, 0(4): 388-394 |
| 作者姓名： | 孔丽华 沈自飞 |
| 作者单位： | 浙江师范大学数理与信息工程学院 |
| 基金项目： | 国家自然科学基金资助项目(10971194) |
| 摘 要： | 研究了带扰动参数的拟线性椭圆方程-ε2△u-ε2△（u2）u＋ε2V（x）u=h（u）,x∈RN,N≥3正解的存在性．其中V（x）为正的连续位势函数．在h（u）及V（x）满足适当的条件下，建立了方程正解的存在性定理． |
| 关 键 词： | 椭圆方程 变分法 临界点 正解 |
The existence of positive solution for the quasilinear elliptic equation with perturbation parameter |
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| KONG Lihua,SHEN Zifei. The existence of positive solution for the quasilinear elliptic equation with perturbation parameter[J]. Journal of Zhejiang Normal University Natural Sciences, 2012, 0(4): 388-394 | |
| Authors: | KONG Lihua SHEN Zifei |
| Affiliation: | (College of Mathematics,Physics and Information Engineering,Zhejiang Normal University,Jinhua Zhejiang 321004,China) |
| Abstract: | It was showed the existence of positive solution for the quasilinear elliptic equation with perturbation parameter as -ε2△u-ε2△（u2）u＋ε2V（x）u=h（u）,x∈RN,N≥3 with V（x） a positive continuous potential function. Under some assumptions on V（x） and the nonlinear term h （ u ）, the existence of positive solution for the above equation was obtained. |
| Keywords: | elliptic equation variational method critical point positive solution |
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