含奇异非线性项与不定势的拟线性椭圆组的解与基态解
偏微分方程分析
2018-11-20 v1
摘要
我们建立了由 ()-拉普拉斯算子驱动的拟线性椭圆组的有界态解与基态解的存在性。此处的主要特点是考虑同时涉及非奇异非线性项与不定势相结合、以及受超线性与次临界耦合项扰动的奇异情形的拟线性椭圆组。这些使得我们无法使用基于 Ambrosetti-Rabinowitz 条件及可微泛函变分方法的论证。通过探索 Nehari 方法并对相关纤维映射进行精细分析，我们得到估计，从而统一论证以展示两种情形下半平凡解的多重性。
引用
@article{arxiv.1811.07360,
title = {Ground and bound state solutions for quasilinear elliptic systems including singular nonlinearities and indefinite potentials},
author = {M. L. M. Carvalho and Edcarlos D. Da Silva and C. A. Santos and C. Goulart},
journal= {arXiv preprint arXiv:1811.07360},
year = {2018}
}
备注
Here we discusse existence and multiplicity of solutions for for quasilinear elliptic systems driven by (\phi 1, \phi 2)-Laplacian operator