一类带p-拉普拉斯算子的分数边值问题的NEHARI流形和多重性结果

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2019-01-01 DOI:10.4134/BKMS.b181172

A. Ghanmi, Ziheng Zhang

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引用次数: 8

摘要

在这项工作中,我们调查以下部分边值问题tD T (| 0 d T (u (T)) | 0 dt u (T)) =∇W (T, u (T)) +λg (T) | u (T) | q−2 u (T) T∈(0,T), u (0) = (T) = 0,∇W (T, u)在哪里的梯度W (T, u) u C和W∈([0,T]×Rn, R)是均匀程度的R,λ是一个积极的参数,g∈C ([0, T]), 1 < R < p < q和p <α< 1。利用纤维映射和Nehari流形，对于某正常数λ0使得0 < λ < λ0，证明了至少两个非平凡解的存在性。

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NEHARI MANIFOLD AND MULTIPLICITY RESULTS FOR A CLASS OF FRACTIONAL BOUNDARY VALUE PROBLEMS WITH p-LAPLACIAN

In this work, we investigate the following fractional boundary value problems  tD T ( |0D t (u(t))|0Dt u(t) ) = ∇W (t, u(t)) + λg(t)|u(t)|q−2u(t), t ∈ (0, T ), u(0) = u(T ) = 0, where ∇W (t, u) is the gradient of W (t, u) at u and W ∈ C([0, T ]×Rn,R) is homogeneous of degree r, λ is a positive parameter, g ∈ C([0, T ]), 1 < r < p < q and 1 p < α < 1. Using the Fibering map and Nehari manifold, for some positive constant λ0 such that 0 < λ < λ0, we prove the existence of at least two non-trivial solutions.

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来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).