Critical Point Theory on Partially Ordered Hilbert Spaces
Critical Point Theory on Partially Ordered Hilbert Spaces
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DOI：
10.1006/jfan.2001.3789
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发表时间：
2001-10
影响因子：
1.7
通讯作者：
T. Bartsch
中科院分区：
文献类型：
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作者：
T. Bartsch
我们发展了一些抽象的临界点理论，以证明在有界区域Ω <$RN，2<p<2N/（N−2）上的边值问题（如模型问题[公式]）有无穷多个变号解±uk，k∈N，它们是不可比较的，即，uk−ul和uk+ul变号，k ∈ l。我们还证明了不存在子解u使得对于某个k u<uk且u在某处为正。相应的不存在性结果适用于上解，相关的结果的存在性的符号变化的解决方案持有其他类的非线性。
We develop some abstract critical point theory in order to prove that boundary value problems like the model problem[formula] on a bounded domain Ω⊂RN, 2<p<2N/(N−2) have infinitely many sign changing solutions ±uk, k∈N, which are not comparable, that is, uk−ul and uk+ul change sign for k≠l. We also show that there are no subsolutions u such that u<uk for some k and u is positive somewhere. A corresponding nonexistence result applies to supersolutions, Related results on the existence of sign-changing solutions hold for other classes of nonlinearities.