Singular Type Trudinger–Moser Inequalities with Logarithmic Weights and the Existence of Extremals

Zhao, Huimin; Guo, Yongqiang; Shen, Yansheng

doi:10.1007/s00009-023-02582-0

Mediterr. J. Math.

2024

DOI: 10.1007/s00009-023-02582-0

|View full text |Cite

Singular Type Trudinger–Moser Inequalities with Logarithmic Weights and the Existence of Extremals

Huimin Zhao,

Yongqiang Guo,

Yansheng Shen

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Elliptic equations in $ \mathbb{R}^2 $ involving supercritical exponential growth

Leuyacc

2024

era

View full text Add to dashboard Cite

In this work, we investigated the existence of nontrivial weak solutions for the equation<disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ -{\rm div}(w(x)\nabla u) \ = \ f(x,u),\qquad x \in \mathbb{R}^2, $\end{document} </tex-math></disp-formula>where $ w(x) $ is a positive radial weight, the nonlinearity $ f(x, s) $ possesses growth at infinity of the type $ {\rm \exp}\big((\alpha_0+h(|x|)\big)|s|^{2/(1-\beta)}) $, with $ \alpha_0 > 0 $, $ 0 < \beta < 1 $ and $ h $ is a continuous radial function that may be unbounded at infinity. To show the existence of weak solutions, we used variational methods and a new type of the Trudinger-Moser inequality defined on the whole two-dimensional space.

show abstract

Elliptic equations in $ \mathbb{R}^2 $ involving supercritical exponential growth

Leuyacc

2024

era

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Singular Type Trudinger–Moser Inequalities with Logarithmic Weights and the Existence of Extremals

Cited by 1 publication

References 24 publications

Elliptic equations in $ \mathbb{R}^2 $ involving supercritical exponential growth

Elliptic equations in $ \mathbb{R}^2 $ involving supercritical exponential growth

Contact Info

Product

Resources

About