Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains☆
Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains☆
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DOI：
10.1016/j.jde.2015.02.040
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发表时间：
2015-08
影响因子：
2.4
通讯作者：
W. Shuai
中科院分区：
文献类型：
--
作者：
W. Shuai
研究了一类有界区域上的Kirchhoff型问题的最小能量变号解的存在性。因为所谓的非局部项B（Ω| u| 2 dx）Δ u的情况下，方程的变分泛函具有与B= 0时完全不同的性质。结合约束变分法和定量变形引理，证明了该问题存在一个最小能量变号解u B.此外，我们还证明了u B的能量严格大于基态能量。最后，我们把B作为参数，给出了当B ≠ 0时u B的一个收敛性质。
We are interested in the existence of least energy sign-changing solutions for a class of Kirchhoff-type problem in bounded domains. Because the so-called nonlocal term b (∫ Ω|∇ u| 2 d x) Δ u is involving in the equation, the variational functional of the equation has totally different properties from the case of b= 0. Combining constraint variational method and quantitative deformation lemma, we prove that the problem possesses one least energy sign-changing solution u b. Moreover, we show that the energy of u b is strictly larger than the ground state energy. Finally, we regard b as a parameter and give a convergence property of u b as b↘ 0.