| 一类椭圆型半变分不等式解的存在性(英文) |
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| 引用本文： | 张金国,刘晓春.一类椭圆型半变分不等式解的存在性(英文)[J].数学杂志,2012,32(4):571-581. |
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| 作者姓名： | 张金国 刘晓春 |
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| 作者单位： | 武汉大学数学与统计学院,湖北武汉,430072 |
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| 基金项目： | NSFC，RFDP，the Fundamental Research Fund for the Central Universities |
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| 摘 要： | 本文研究了一类Dirichlet边界的椭圆型半变分不等式问题.利用非光滑形式的环绕定理和非光滑形式的对称山路定理,得到了在相应假设条件下此不等式问题至少有一个非平凡解和无穷多解.本文中非光滑势能在原点处关于算子+V(x)的第一正特征值λ是不完全共振的.
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| 关 键 词： | 半变分不等式 非光滑环绕定理 非光滑对称山路定理 |
THE EXISTENCE OF SOLUTIONS FOR A CLASS OF ELLIPTIC HEMIVARIATIONAL INEQUALITY |
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| ZHANG Jin-guo
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LIU Xiao-chun.THE EXISTENCE OF SOLUTIONS FOR A CLASS OF ELLIPTIC HEMIVARIATIONAL INEQUALITY[J].Journal of Mathematics,2012,32(4):571-581. |
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| Authors: | ZHANG Jin-guo LIU Xiao-chun |
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| Institution: | (School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China) |
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| Abstract: | In this paper,we study hemivariational inequality with a nonlinear Dirichlet elliptic problem.By using a nonsmooth linking theorem and nonsmooth symmetric mountain pass theorem,we prove the existence of a nontrivial solution and infinitely many distinct solutions.The hypotheses on the nonsmooth potential allow us to have incomplete resonance at 0 with respect to the first positive eigenvalue λk>0 of operator -△+V(x). |
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| Keywords: | hemivariational inequality nonsmooth linking theory non-smooth symmetric mountain pass theorem |
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