A perturbation method in critical point theory and applications
A perturbation method in critical point theory and applications
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DOI：
10.1090/s0002-9947-1981-0621969-9
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发表时间：
1981
影响因子：
1.3
通讯作者：
A. Bahri;H. Berestycki
中科院分区：
文献类型：
--
作者：
A. Bahri;H. Berestycki
本文研究一类非线性椭圆型方程-Au =| u|在P»中，u = 0。这里，sc R^是光滑的和有界的，并且给出了h e L2（Q）。证明了存在pN > 1使得对任意pe（1，pN）和任意hel 2（1 ~ 2），上述方程有无穷多个不同的解.该方法依赖于一个特征的临界值的存在性，通过某些水平集的noncontractibility属性。一个扰动参数使人们能够使用一些相关的甚至功能的性质。这种方法的其他几个应用程序也被提出。
This paper is concerned with existence and multiplicity results for nonlinear elliptic equations of the type -Au = |u|''_1u + h(x) in P», u = 0 on 3s. Here, s c R^ is smooth and bounded, and h e L2(Q) is given. We show that there exists pN > 1 such that for any p e (\,pN) and any h e L2(I2), the preceding equation possesses infinitely many distinct solutions. The method rests on a characterization of the existence of critical values by means of noncontractibility properties of certain level sets. A perturbation argument enables one to use the properties of some associated even functional. Several other applications of this method are also presented.