具有可变指数的双相问题取决于整个空间RN的解和梯度

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-02-14 DOI:10.1016/j.nonrwa.2025.104334

Ala Eddine Bahrouni , Anouar Bahrouni , Patrick Winkert

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引用次数: 0

摘要

在本文中，我们建立了一类新的Musielak-Orlicz Sobolev空间在依赖于未知解及其梯度的变指数双相位算子驱动的无界域上的连续紧嵌入。利用这些嵌入和一个抽象的关键点定理，我们证明了与这个新算子相关的这些问题在整个空间Rd中的弱解的存在性和多重性。这项工作可以看作是bahroui - bahroui - missaoui - ruridulescu （bahroui et al., 2024）最近论文的延续。

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Double phase problems with variable exponents depending on the solution and the gradient in the whole space RN

In this paper, we establish continuous and compact embeddings for a new class of Musielak-Orlicz Sobolev spaces in unbounded domains driven by a double phase operator with variable exponents that depend on the unknown solution and its gradient. Using these embeddings and an abstract critical point theorem, we prove the existence and multiplicity of weak solutions for such problems associated with this new operator in the whole space

R^{d}

. This work can be seen as a continuation of the recent paper by Bahrouni–Bahrouni–Missaoui–Rădulescu (Bahrouni et al., 2024).

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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.