Musielak-Orlicz空间中非线性抛物方程周期问题的变分方法

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-03-23 DOI:10.1016/j.nonrwa.2025.104375

A. Nowakowski , E. Öztürk

引用次数: 0

摘要

讨论了一类非线性抛物方程的周期问题，其形式为：(1)xt(t)−Ax(t)+Hxx(t)−Qx(x(t))=0，其中a是广义模空间中的非线性算子；H和Q是凸泛函。我们提出了一种新的基于fenchell - young共轭的变分方法来证明周期解的存在性。然后，我们将抽象结果应用于Musielak-Orlicz空间中的非线性抛物方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Variational approach to the periodic problem for a nonlinear parabolic equation in Musielak–Orlicz spaces

We discuss the periodic problem for a nonlinear parabolic equation of the form: (1)

x_{t} (t) - A x (t) + H_{x} (x (t)) - Q_{x} (x (t)) = 0

where

A

is a nonlinear operator in a generalized modular space;

H

and

Q

are convex functionals. We derive a new variational method based on the Fenchel–Young conjugacy to prove the existence of periodic solutions. Next, we apply the abstract result to a nonlinear parabolic equation in Musielak–Orlicz spaces.

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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.