NDLI: On a Brezis–Nirenberg type quasilinear problem

Content Provider	Springer Nature Link
Author	Guo, Yuxia Liu, Jiaquan Wang, Zhi Qiang
Copyright Year	2016
Abstract	In this paper, we consider the following quasilinear equation with critical exponent, a quasilinear version of the classical Brezis–Nirenberg problem: $$\begin{aligned} \left\{ \begin{array}{rlll} -\displaystyle \sum _{i, j=1}^ND_j(a_{ij}(u)D_i u)+\frac{1}{2}\displaystyle \sum _{i, j=1}^Na'_{ij}(u)D_i uD_j u &{}= au+\|u\|^{2^-2}u &{} \quad \hbox { in } \Omega \\ u&{}=0 &{} \quad \hbox { on } \partial \Omega ,\\ \end{array}\right. \quad {(P)} \end{aligned}$$ where $$ 2^=\frac{2N}{N-2}$$ is the Sobolev critical exponent for the embedding of $$H_0^1(\Omega )$$ into $$L^p(\Omega )$$ , $$\Omega \subset \mathbb {R}^N$$ is an open-bounded domain with smooth boundary, $$a>0$$ is a constant. We prove that if $$N\ge 7,$$ the problem (P) admits an unbounded sequence of solutions. These solutions are obtained from subcritical approximations. This is done by analyzing the asymptotic behavior and the concentration compactness of the approximation solutions for the subcritical problems. The existence of infinitely many solutions to the subcritical problems is obtained via a p-Laplacian regularization process.
Starting Page	719
Ending Page	753
Page Count	35
File Format	PDF
ISSN	16617738
Journal	Journal of Fixed Point Theory and Applications
Volume Number	19
Issue Number	1
e-ISSN	16617746
Language	English
Publisher	Springer International Publishing
Publisher Date	2016-11-12
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Quasilinear equations critical exponents multiple bound state solutions A priori estimates Boundary value problems for second-order elliptic equations Mathematics Analysis Mathematical Methods in Physics
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology Applied Mathematics Modeling and Simulation

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

An improved bound for the non-existence of radial solutions of the Brezis-Nirenberg problem in Hn

A Non-Existence Result for a Generalized Radial Brezis-Nirenberg Problem

The solution gap of the Brezis–Nirenberg problem on the hyperbolic space

Ground states of critical and supercritical problems of Brezis–Nirenberg type

The solution gap of the Brezis-Nirenberg problem on the hyperbolic space

On the Brezis-Nirenberg type critical problem for nonlinear Choquard equation

Ground states of critical and supercritical problems of Brezis-Nirenberg type

The second bifurcation branch for radial solutions of the Brezis-Nirenberg problem in dimension four

Multispike solutions for the Brezis-Nirenberg problem in dimension three

On a Brezis–Nirenberg type quasilinear problem

Similar Documents

An improved bound for the non-existence of radial solutions of the Brezis-Nirenberg problem in Hn

A Non-Existence Result for a Generalized Radial Brezis-Nirenberg Problem

The solution gap of the Brezis–Nirenberg problem on the hyperbolic space

Ground states of critical and supercritical problems of Brezis–Nirenberg type

The solution gap of the Brezis-Nirenberg problem on the hyperbolic space

On the Brezis-Nirenberg type critical problem for nonlinear Choquard equation

Ground states of critical and supercritical problems of Brezis-Nirenberg type

The second bifurcation branch for radial solutions of the Brezis-Nirenberg problem in dimension four

Multispike solutions for the Brezis-Nirenberg problem in dimension three

On a Brezis–Nirenberg type quasilinear problem