Positive solution for a quasilinear equation with critical growth in $ℝ^N$

• Autorzy: Lin Chen , Caisheng Chen , Zonghu Xiu
• Języki publikacji: EN

Abstrakty

EN

We study the existence of positive solutions of the quasilinear problem
⎧ $-Δ_N u + V(x)|u|^{N-2}u = f(u,|∇u|^{N-2}∇u)$, $x ∈ ℝ^N$,
⎨
⎩ u(x) > 0, $x∈ ℝ^N$,
where $Δ_N u = div(|∇u|^{N-2}∇u)$ is the N-Laplacian operator, $V:ℝ^N → ℝ$ is a continuous potential, $f:ℝ × ℝ^N → ℝ$ is a continuous function. The main result follows from an iterative method based on Mountain Pass techniques.

Kategorie tematyczne

• 35J20: Variational methods for second-order elliptic equations
• 35J62: Quasilinear elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2016
• Tom: 116
• Numer: 3
• Strony: 251-262

Daty

wydano

2016

Twórcy

autor

Lin Chen

• College of Science, Hohai University, 210098 Nanjing, P.R. China
• College of Mathematics and Statistics, Yili Normal University, 835000 Yining, P.R. China

autor

Caisheng Chen

• College of Science, Hohai University, 210098 Nanjing, P.R. China

autor

Zonghu Xiu

• Science and Information College, Qingdao Agricultural University, 266109 Qingdao, P.R. China

Identyfikatory

DOI

10.4064/ap3664-1-2016