关于涉及零质量和特鲁丁格-莫泽非线性的 (2,q)- 拉普拉斯平面方程

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2024-09-25 DOI:10.1016/j.nonrwa.2024.104227

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引用次数: 0

摘要

在这项工作中，我们研究了 R2 中零质量情况下一类 (2,q) -方程正解的存在性。我们建立了一个加权索波列夫嵌入，并引入了一个新的特鲁丁格-莫泽式不等式。此外，由于我们在合适的径向索波列夫空间上工作，我们证明了帕莱斯著名的对称临界原理的适当版本。最后，我们研究了应用 Moser 迭代方案求解的正则性。

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On a planar equation involving (2,q)-Laplacian with zero mass and Trudinger–Moser nonlinearity

In this work, we study existence of positive solutions to a class of

(2, q)

-equations in the zero mass case in

R^{2}

. We establish a weighted Sobolev embedding and we introduce a new Trudinger–Moser type inequality. Moreover, since we work on a suitable radial Sobolev space, we prove an appropriate version of the well-known Symmetric Criticality Principle by Palais. Finally, we study regularity of solutions applying Moser iteration scheme.

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.