Infinitely many arbitrarily small positive solutions for the Dirichlet problem involving the p-Laplacian
Infinitely many arbitrarily small positive solutions for the Dirichlet problem involving the p-Laplacian
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DOI：
10.1017/s030821050000175x
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发表时间：
2002-06
期刊：
影响因子：
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通讯作者：
G. Anello;G. Cordaro
中科院分区：
文献类型：
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作者：
G. Anello;G. Cordaro
本文给出了如下p-Laplacian Dirichlet问题存在无穷多个任意小正解的一个结果，其中Ω ∈ RN是具有充分光滑边界的有界开集<$Ω，p > 1，λ > 0，f：Ω × R → R是满足下列条件的Carathéodory函数：存在t ∈ 0，使得精确地说，我们的结果保证了a. e.证明了上述问题的弱正解，在L∞（Ω）中收敛到零.
In this paper we present a result of existence of infinitely many arbitrarily small positive solutions to the following Dirichlet problem involving the p-Laplacian, where Ω ∈ RN is a bounded open set with sufficiently smooth boundary ∂Ω, p > 1, λ > 0, and f: Ω × R → R is a Carathéodory function satisfying the following condition: there exists t̄ > 0 such that Precisely, our result ensures the existence of a sequence of a.e. positive weak solutions to the above problem, converging to zero in L∞(Ω).