2020

DOI: 10.1007/s10473-020-0523-9

|View full text |Cite

|

Sign up to set email alerts

|

Positive Solutions and Infinitely Many Solutions for a Weakly Coupled System

¹

,

²

,

³

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Existence Of Second and Third Solutions1

Citation Types

Supporting

0

Mentioning

1

Contrasting

0

Year Published

2021

2021

2022

2022

Publication Types

Select...

Article3

Relationship

Self Cite1

Independent2

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 18 publications

Supporting

0

Mentioning

1

Contrasting

0

Order By: Relevance

“…Proof Let

false{false(u_{n}, v_{n} false) false} \subset {scriptN}_{0}

be such that

{scriptJ}_{0} false(u_{n}, v_{n} false) = \frac{1}{N} S_{α, β}^{\frac{N}{2}} + o_{n} false(1 false)

. In a fashion similar to the argument in Duan et al, 21, lemma 3.1 we infer that

{scriptJ}_{0}^{'} false(u_{n}, v_{n} false) \to 0

. So, {( u n , v n )} is a Palais–Smale sequence of

{scriptJ}_{0}

at the level

\frac{1}{N} S_{α, β}^{\frac{N}{2}}

.…”

Section: Existence Of Second and Third Solutionsmentioning

confidence: 60%

Multiple solutions for critical nonhomogeneous elliptic systems in noncontractible domain

¹

,

²

,

³

2021

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

The paper is concerned with multiple solutions of a nonhomogeneous elliptic system with Sobolev critical exponent over a noncontractible domain, precisely, a smooth bounded annular domain. We prove the existence of four solutions using variational methods and Lusternik–Schnirelmann theory, when the inner hole of the annulus is sufficiently small.

“…Proof Let

false{false(u_{n}, v_{n} false) false} \subset {scriptN}_{0}

be such that

{scriptJ}_{0} false(u_{n}, v_{n} false) = \frac{1}{N} S_{α, β}^{\frac{N}{2}} + o_{n} false(1 false)

. In a fashion similar to the argument in Duan et al, 21, lemma 3.1 we infer that

{scriptJ}_{0}^{'} false(u_{n}, v_{n} false) \to 0

. So, {( u n , v n )} is a Palais–Smale sequence of

{scriptJ}_{0}

at the level

\frac{1}{N} S_{α, β}^{\frac{N}{2}}

.…”

Section: Existence Of Second and Third Solutionsmentioning

confidence: 60%

Multiple solutions for critical nonhomogeneous elliptic systems in noncontractible domain

¹

,

²

,

³

2021

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

The paper is concerned with multiple solutions of a nonhomogeneous elliptic system with Sobolev critical exponent over a noncontractible domain, precisely, a smooth bounded annular domain. We prove the existence of four solutions using variational methods and Lusternik–Schnirelmann theory, when the inner hole of the annulus is sufficiently small.

Periodic and almost periodic solutions for a non-autonomous respiratory disease model with a lag effect

¹

,

²

,

³

2021

Acta Math Sci

View full text Add to dashboard Cite

No abstract

Existence of ground state for coupled system of biharmonic Schrödinger equations

Wang¹,

Liu²,

³

2022

View full text Add to dashboard Cite

<abstract><p>In this paper we consider the following system of coupled biharmonic Schrödinger equations</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \ \left\{ \begin{aligned} \Delta^{2}u+\lambda_{1}u = u^{3}+\beta u v^{2}, \\ \Delta^{2}v+\lambda_{2}v = v^{3}+\beta u^{2}v, \end{aligned} \right. \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>where $ (u, v)\in H^{2}({\mathbb{R}}^{N})\times H^2(\mathbb R^N) $, $ 1\leq N\leq7 $, $ \lambda_{i} > 0 (i = 1, 2) $ and $ \beta $ denotes a real coupling parameter. By Nehari manifold method and concentration compactness theorem, we prove the existence of ground state solution for the coupled system of Schrödinger equations. Previous results on ground state solutions are obtained in radially symmetric Sobolev space $ H_r^2(\mathbb R^N)\times H_r^2(\mathbb R^N) $. When $ \beta $ satisfies some conditions, we prove the existence of ground state solution in the whole space $ H^2(\mathbb R^N)\times H^2(\mathbb R^N) $.</p></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

Product

Browser Extension Assistant by scite Citation Statement Search Reference Check Visualizations Dashboards Explore Journals Explore Organizations Explore Funders Embedding Badge Embedding Citation Search Pricing

Resources

Blog Help & FAQ Accessibility Statement API Terms For Universities & Governments For Researchers For Publishers For Corporate, Pharma & Enterprise Author Marketing Become an Affiliate Get an organization trial or quote scite Data & Services

About

News & Press Careers Read our Paper Coverage

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

Copyright © 2025 scite LLC. All rights reserved.

Made with 💙 for researchers

Part of the Research Solutions Family.