Some results on the p(u)-Laplacian problem
Some results on the p(u)-Laplacian problem
复制标题
DOI：
10.1007/s00208-019-01803-w
复制
发表时间：
2019-10
影响因子：
1.4
通讯作者：
M. Chipot;H. B. de Oliveira
中科院分区：
文献类型：
--
作者：
M. Chipot;H. B. de Oliveira
本文考虑了具有依赖于解本身的非线性指数的p-Laplace问题。本文研究了p(U)为局域量和p(U)为非局域量的两种情况。对于相关的边值局部问题，我们利用奇异摄动技巧证明了弱解的存在性。我们还证明了相关边值问题的非局部形式弱解的存在性。本文还讨论了这些问题的唯一性问题，特别是通过计算一维局部问题的唯一性，并证明了唯一性在非局部问题中很容易丢失。
Thep-Laplacian problem with the exponent of nonlinearitypdepending on the solutionuitself is considered in this work. Both situations whenp(u) is a local quantity or whenp(u) is nonlocal are studied here. For the associated boundary-value local problem, we prove the existence of weak solutions by using a singular perturbation technique. We also prove the existence of weak solutions to the nonlocal version of the associated boundary-value problem. The issue of uniqueness for these problems is addressed in this work as well, in particular by working out the uniqueness for a one dimensional local problem and by showing that the uniqueness is easily lost in the nonlocal problem.