Infinitely many solutions for p-Laplacian equation involving critical Sobolev growth

By Daomin Cao, Shuangjie Peng, Shusen Yan. 2012

126 citations recorded by the source corpus.

In this paper, we will prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth: −Δpu=|u|p⁎−2u+μ|u|p−2uin Ω,u=0on ∂Ω, provided N>p2+p, where Δp is the p-Laplacian operator, 1 0 and Ω is an open bounded domain in RN.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/373877599d18f7a53fe729f54ac2f8d69dc8eb5e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations (2015, background): “The role of Pohozaev identity in the existence and nonexistence of solutions to problems with critical Sobolev exponents has been showed in many papers, see [6, 12, 13, 32] and the references therein.”
On Dirichlet problem for fractional p-Laplacian with singular non-linearity (2016, background): “Among the works dealing with elliptic equations with singular and critical growth terms, we cite [1, 2, 9, 25, 34, 40], see also the references therein, with no attempt to provide a complete list.”
Equations involving fractional Laplacian operator: Compactness and application (2015, methodology): “3), similarly to [12], we can deduce that if N > 4α, then”
Asymptotic behaviors of solutions to quasilinear elliptic equations with critical Sobolev growth and Hardy potential (2015, background): “[3, 4, 7, 8, 9, 10, 11, 16, 17, 19, 20, 26].”