具有Hardy-Sobolev指数的临界双相h问题的存在性结果

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-12-24 DOI:10.1016/j.cnsns.2024.108551

Yu Cheng, Zhanbing Bai

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引用次数: 0

摘要

本文考虑了具有Hardy-Sobolev指数的临界双相hsamnon问题的可解性。在适当的假设条件下，通过纤维化方法得到了该问题至少有一个弱解的存在性，其形式为Nehari流形。为了克服Musielak-Orlicz-Sobolev空间中由于临界增长而导致的紧性不足，分析了梯度的收敛性，其中涉及到一些基本不等式和截断方法。

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Existence results for critical double phase Hénon problems with Hardy–Sobolev exponent

Herein, the solvability of the critical double phase Hénon problem with a Hardy–Sobolev exponent is considered. Under some appropriate assumptions, the existence of at least one weak solution is obtained via the fibering method in form of the Nehari manifold. To overcome the lack of compactness arising from critical growth in the Musielak–Orlicz–Sobolev space, the convergence of gradients is analyzed, which involves some basic inequalities and truncation methods.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.