Least energy solutions for indefinite biharmonic problems via modified Nehari–Pankov manifold
Least energy solutions for indefinite biharmonic problems via modified Nehari–Pankov manifold
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DOI：
10.1142/s021919971750047x
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发表时间：
2017-04
影响因子：
1.6
通讯作者：
Miaomiao Niu;Z. Tang;Lushun Wang
中科院分区：
文献类型：
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作者：
Miaomiao Niu;Z. Tang;Lushun Wang
本文利用修正的Nehari-Pankov流形证明了不定双调和方程Δ2u+(λV(X)−δ(X))u=|u|p−2u inℝN，(Pλ)的最小能量解的存在性和渐近性，其中N≥5，2 0是参数，V(X)是具有非空零集的非负势函数，−1(0)，δ(X)是正函数，使得算子Δ2+λV(X)−δ(X)对于λ大是不定且非退化的。我们证明了在亚临界和临界情况下，方程(Pλ)都存在一个最小能量解，该最小能量解对于λ>；0在−1(0)的零点附近有很大的局部化。
In this paper, by using a modified Nehari–Pankov manifold, we prove the existence and the asymptotic behavior of least energy solutions for the following indefinite biharmonic equation: Δ2u + (λV (x) − δ(x))u = |u|p−2uinℝN, (P λ) where N ≥ 5, 2 0 is a parameter, V (x) is a nonnegative potential function with nonempty zero set intV−1(0), δ(x) is a positive function such that the operator Δ2 + λV (x) − δ(x) is indefinite and non-degenerate for λ large. We show that both in subcritical and critical cases, equation (Pλ) admits a least energy solution which for λ > 0 large localized near the zero set intV−1(0).