Infinitely many solutions for the Schrödinger equations in ℝᴺ with critical growth

Wenyi Chen; Juncheng Wei; Shusen Yan

doi:10.1016/j.jde.2011.09.032

Infinitely many solutions for the Schrödinger equations in ℝᴺ with critical growth

Wenyi Chen
, Juncheng Wei
, Shusen Yan

Mathematics

Research output: Contribution to journal › Article › peer-review

75 Citations (Scopus)

Abstract

We consider the following nonlinear problem in ℝᴺ ... where V (r) is a bounded non-negative function, N ≥ 5. We show that if r²V (r) has a local maximum point, or local minimum point r0 >0 with V (r0) > 0, then (0.1) has infinitely many non-radial solutions, whose energy can be made arbitrarily large.

Original language	English
Pages (from-to)	2425-2447
Journal	Journal of Differential Equations
Volume	252
Issue number	3
DOIs	https://doi.org/10.1016/j.jde.2011.09.032
Publication status	Published - 2012

Keywords

Partial Differential Equations

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10.1016/j.jde.2011.09.032

https://hdl.handle.net/1959.11/11639

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title = "Infinitely many solutions for the Schr{\"o}dinger equations in ℝᴺ with critical growth",

abstract = "We consider the following nonlinear problem in ℝᴺ ... where V (r) is a bounded non-negative function, N ≥ 5. We show that if r²V (r) has a local maximum point, or local minimum point r0 >0 with V (r0) > 0, then (0.1) has infinitely many non-radial solutions, whose energy can be made arbitrarily large.",

keywords = "Partial Differential Equations",

author = "Wenyi Chen and Juncheng Wei and Shusen Yan",

year = "2012",

doi = "10.1016/j.jde.2011.09.032",

language = "English",

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issn = "0022-0396",

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T1 - Infinitely many solutions for the Schrödinger equations in ℝᴺ with critical growth

AU - Chen, Wenyi

AU - Wei, Juncheng

AU - Yan, Shusen

PY - 2012

Y1 - 2012

N2 - We consider the following nonlinear problem in ℝᴺ ... where V (r) is a bounded non-negative function, N ≥ 5. We show that if r²V (r) has a local maximum point, or local minimum point r0 >0 with V (r0) > 0, then (0.1) has infinitely many non-radial solutions, whose energy can be made arbitrarily large.

AB - We consider the following nonlinear problem in ℝᴺ ... where V (r) is a bounded non-negative function, N ≥ 5. We show that if r²V (r) has a local maximum point, or local minimum point r0 >0 with V (r0) > 0, then (0.1) has infinitely many non-radial solutions, whose energy can be made arbitrarily large.

KW - Partial Differential Equations

U2 - 10.1016/j.jde.2011.09.032

DO - 10.1016/j.jde.2011.09.032

M3 - Article

SN - 0022-0396

VL - 252

SP - 2425

EP - 2447

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 3

ER -

Infinitely many solutions for the Schrödinger equations in ℝᴺ with critical growth

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Keywords

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