| 关于一类半线性椭圆型方程存在无穷多解的注记 |
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| 引用本文： | 耿堤,秦成林.关于一类半线性椭圆型方程存在无穷多解的注记[J].兰州大学学报(自然科学版),1992(3). |
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| 作者姓名： | 耿堤 秦成林 |
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| 作者单位： | 兰州大学数学系 兰州730000
(耿堤)，兰州大学数学系 兰州730000(秦成林) |
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| 摘 要： | 本文考虑 n 维空间中有界光滑区域上的一类半线性椭圆型方程的边值问题.方程含有两项非线性项,第一项为奇函数具有次线性增长阶,第二项是超线性增长阶的非奇性扰动.证明了在适当的条件下无穷多个解的存在性.类似的问题已有过讨论,但这里直接考虑较一般的情形,并且所用的方法也与之不同.
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| 关 键 词： | 非线性椭圆型方程 摄动 临界值 无穷多解 |
A Note on the Existence of Infinitely Many Solutions for a Class of Semilinear Elliptic Equations |
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| Geng Di,Qin Chenglin.A Note on the Existence of Infinitely Many Solutions for a Class of Semilinear Elliptic Equations[J].Journal of Lanzhou University(Natural Science),1992(3). |
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| Authors: | Geng Di Qin Chenglin |
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| Abstract: | In this paper,a class of semilinear elliptic type equations areconsidered on a bounded and smooth domain of n-dimension space.There are two nonlinear terms in the equations:one of them isa sublinear odd function,and the other a superlinear increase non-oddperturbation.It is proved that there exist infinitely many solutions forthe equations under some conditions.An extraordinary method is usedin the proof which is different from others;the conditions posed in thepaper are more general and reasonable. |
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| Keywords: | nonlinear elliptic equations perturbation critical value infinitely many solutions |
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