Fast and Slow Decaying Solutions of Lane–Emden Equations Involving Nonhomogeneous Potential-Reference-Cited by-同舟云学术

Fast and Slow Decaying Solutions of Lane–Emden Equations Involving Nonhomogeneous Potential

Published:2020-02-05 Issue:2 Volume:20 Page:339-359
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Chen Huyuan¹,Huang Xia²,Zhou Feng²

Affiliation:

1. Department of Mathematics , Jiangxi Normal University , Nanchang , Jiangxi 330022 , P. R. China

2. Center for PDEs , School of Mathematical Sciences , East China Normal University , Shanghai Key Laboratory of PMMP , Shanghai 200241 , P. R. China

Abstract

Abstract Our purpose in this paper is to study positive solutions of the Lane–Emden equation

- Δ ⁢ u = V ⁢ u p in ⁢ ℝ N ∖ { 0 } ,

-\Delta u=Vu^{p}\quad\text{in }\mathbb{R}^{N}\setminus\{0\},

perturbed by a nonhomogeneous potential V, with p ∈ ( N N - 2 , p c )

p\in(\frac{N}{N-2},p_{c})

, where p c

{p_{c}}

is the Joseph–Ludgren exponent. We construct a sequence of fast and slow decaying solutions with appropriated restrictions for V.

Funder

National Natural Science Foundation of China

National Science Foundation

Science and Technology Commission of Shanghai Municipality

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2020-2071/pdf

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