非局部临界椭圆问题的多重性结果

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-09-23 DOI:10.1112/blms.13156

Said El Manouni, Kanishka Perera

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引用次数: 0

摘要

在有界区域上证明了一类非局部临界增长椭圆型问题的新的多重性结果。更具体地说，我们证明了这里所考虑的问题对于某参数λ ＆gt的所有足够大的值都有任意多个解；0 $\lambda > 0$。特别地，当λ→∞$\lambda \rightarrow \infty$时，解的个数趋于无穷。我们还给出了λ $\lambda$的显式下界，以便得到给定数量的解。这个下界是用相关的非局部椭圆算子的特征值序列表示的。这些证明是基于一个抽象的临界点定理。

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Multiplicity results for nonlocal critical elliptic problems

We prove new multiplicity results for some nonlocal critical growth elliptic problems in bounded domains. More specifically, we show that the problems considered here have arbitrarily many solutions for all sufficiently large values of a certain parameter $λ > 0$ . In particular, the number of solutions goes to infinity as $λ \to \infty$ . We also give an explicit lower bound on $λ$ in order to have a given number of solutions. This lower bound is in terms of a sequence of eigenvalues of the associated nonlocal elliptic operator. The proofs are based on an abstract critical point theorem.