ABSTRACT

In this paper, we study the existence of solutions for non-coercive variational-hemivariational inequalities involving nonlocal fractional p-Laplacian. Our approach is based on the theory of pseudomonotone operators in the sense of Brézis, recession analysis and the properties of nonlocal fractional p-Laplace operators recently established.The innovation of this paper is that we do not assume the usual coercivity or smallness assumptions as stated in most existing literature. The absence of such assumptions will make the existence of solutions very complicated. We have to proceed from the specific problem itself and seek specific methods based on the inherent characteristics of different problems.

摘要

在本文中，我们研究了涉及非局部分数 p-拉普拉斯算子的非强制变分半变分不等式的解的存在性。我们的方法基于 Brézis 意义上的伪单调算子理论、衰退分析和最近建立的非局部分数 p-拉普拉斯算子的性质。本文的创新之处在于我们没有假设通常的矫顽力或小假设。在大多数现有文献中。缺乏这样的假设将使解决方案的存在变得非常复杂。我们要从具体问题本身出发，根据不同问题的内在特点，寻求具体的方法。