|Table of Contents|

Multiple Solutions of a Schr?inger Equation with Indefinite Nonlinearity(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2021年03期
Page:
9-13
Research Field:
·数学·
Publishing date:

Info

Title:
Multiple Solutions of a Schr?inger Equation with Indefinite Nonlinearity
Author(s):
Hong Mingli1; Li Linrui1; Huang Daiwen2
(1.Institute of Disaster Prevention,Sanhe 065201,China)(2.Institute of Applied Physics and Computational Mathematics,Beijing 100088,China)
Keywords:
Schr?inger equation; indefinite nonlinearity; radial solutions
PACS:
O177
DOI:
10.3969/j.issn.1001-4616.2021.03.002
Abstract:
In this paper,we consider the following Schr?inger equation:-Δu=V(|x|)u+f(|x|,u),x∈RN,u∈H1(RN). Under some assumptions of V and f,we obtain infinitely many radial solutions of the above equation.

References:

[1] BARTSCH T,WILLEM M. Infinitely many nonradial solutions of a Euclidean scalar field equation[J]. Journal of functional analysis,1993,117:447-460.
[2]STRUWE M. Multiple solutions of differential equations without the Palais-Smale condition[J]. Mathematische annalen,1992,261:339-412.
[3]STRAUSS W A. Existence of solitary waves in higher dimensions[J]. Communications in mathematical physics,1977,55:149-162.
[4] ALAMA S,DEL PINO M. Solutions of elliptic equations with indefinite nonlinearities via Morse theory and linking[J]. Annales DE L insttitut henri poincare-analyse nonlineaire,1996,13:95-115.
[5]BADIALE M,NABANA E. A remark on multiplicity of solutions for semilinear elliptic problems with indefinite nonlinearity[J]. Comptes rendus deI’sAcadémie des sciences-series I-mathematics,1996,323(2):151-156.
[6]LI Y Q,CHEN J Q. On a semilinear elliptic equation with indefinite linear part[J]. Nonlinear analysis,2002,48:399-410.
[7]CHEN J Q,LI S J. Existence and multiplicity of nontrivial solutions for elliptic equation on RN with indefinite linear part[J]. Manuscripta mathematica,2003,111:221-239.
[8]COSTA D,TEHRANI H. Existence of positive solutions for a class of indefinite elliptic problems in RN with indefinite linear part[J]. Manuscripta mathematica,2003,111:221-239.
[9]COSTA D,TEHRANI H. Existence of positive solutions for a class of indefinite elliptic problems in . Calculus of variations and partial differential equations,2001,13:159-189.
[10]WILLEM M. Minimax Theorems[M]. Birkh?ser:Boston,1996.
[11]PALAIS R S. The principle of symmetric criticality[J]. Communications in mathematical physics,1979,69:19-30.

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Last Update: 2021-09-15