学术
摘 要:
讨论一个含临界位势的广义平均曲率方程在Dirichlet边界条件下解的存在性．此方程相应的变分泛函关于“的梯度非齐次，且Sobolev空间嵌入失去紧性．为了克服这些困难，本文将关于范数的一个基本结论推广到一般的偶泛函，并利用C．K．N不等式及Ambrosetti的山路引理证明了方程存在非平凡解．[著者文摘]
文章出处:
《应用数学》-2006年19卷1期 -110-119页
分 类 号:
文献标识码:
A
文章编号:
1001-9847（2006）01-0110-10
Solutions of a Generalized Mean Curvature Equation with Critical Potential
YANG Jun, SHEN Yao-tian （School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China）
Abstract:
This paper studies the existence of the solutions of a generalized mean curvature equation with critical potential under the Dirichlet boundary condition. The gradient of u in the corresponding variational functional of this equation is nonhomogeneous and the embedding into the Sobolev space lacks of compactness. In order to solve the difficulties,we extend a lemma about norm into the case of generalized even functionals. The existence of the nontrivial solutions is proved with the Mountain Pass lemma and the C. K. N. inequality.[著者文摘]
Key words:
C. K. N. inequality; Critical potential; （PS）c conditions; Mountain Pass lemma
基金资助:
国家自然科学基金资助项目（10471047）及广东省自然科学基金资助项目（011606）
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