由$\mathbb{R}^N$中非标准拉普拉斯算子驱动的拟线性包含系统的三个解

中文摘要 AI 辅助

本文证明了在无界域$\mathbb{R}^{N}$上的Orlicz-Sobolev空间中，由局部Lipschitz泛函控制的一类非齐次拟线性包含系统存在三个不同的弱解。通过利用Wu-Zhou在[29]中建立的一个新的三临界点定理，我们将非光滑临界点理论扩展到处理具有非线性增长的情形。该分析对非线性项$H$施加了一个精确的结构条件，要求其表现出超线性增长，同时保持次临界渐近行为。这一条件在增长限制与泛函分析要求之间建立了微妙的平衡。本工作的新颖之处包括构造了与Orlicz-Sobolev空间结构及非线性增长特征相一致的合适能量泛函。通过严格的变分分析和精细的估计技术，我们在这些广义条件下建立了三个弱解的存在性，从而显著扩展了临界点方法在非标准函数空间中的适用性。

英文摘要

This paper establishes the existence of three distinct weak solutions for a class of nonhomogeneous quasilinear inclusion systems, which are governed by locally Lipschitz functionals within Orlicz-Sobolev spaces over unbounded domains $\mathbb{R}^{N}$.By employing a new three critical points theorem established by Wu-Zhou in [29], we extend the nonsmooth critical point theory to handle scenarios with nonlinear growth conditions.Our analysis imposes a precise structural condition on the nonlinear term $H$, requiring it to exhibit superlinear growth while maintaining subcritical asymptotic behavior. This condition establishes a delicate balance between growth restrictions and functional analytic requirements. The novelties of this work include the construction of suitable energy functionals that are consistent with both the structure of Orlicz-Sobolev spaces and the characteristics of nonlinear growth. Through rigorous variational analysis and careful estimation techniques, we establish the existence of three weak solutions under these generalized conditions, thereby significantly expanding the applicability of critical point methods in nonstandard function spaces.

发表机构

• Kunming University of Science and Technology（昆明理工大学）
• Research Center for Mathematics and Interdisciplinary Sciences, Kunming University of Science and Technology（昆明理工大学数学与交叉科学研究中心）

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