A sign-changing solution for a superlinear Dirichlet problem

Alfonso Castro, Jorge Cossio, John M. Neuberger

Research output: Contribution to journalArticle

170 Citations (Scopus)

Abstract

We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the sign-changing solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].

Original languageEnglish (US)
Pages (from-to)1041-1053
Number of pages13
JournalRocky Mountain Journal of Mathematics
Volume27
Issue number4
StatePublished - Sep 1997

Fingerprint

Sign-changing Solutions
Dirichlet Problem
Morse Index
Sign Change
Nontrivial Solution
Complement
Boundary Value Problem

Keywords

  • Deformation lemma
  • Dirichlet problem
  • Sign-changing solution
  • Subcritical
  • Superlinear

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A sign-changing solution for a superlinear Dirichlet problem. / Castro, Alfonso; Cossio, Jorge; Neuberger, John M.

In: Rocky Mountain Journal of Mathematics, Vol. 27, No. 4, 09.1997, p. 1041-1053.

Research output: Contribution to journalArticle

Castro, Alfonso ; Cossio, Jorge ; Neuberger, John M. / A sign-changing solution for a superlinear Dirichlet problem. In: Rocky Mountain Journal of Mathematics. 1997 ; Vol. 27, No. 4. pp. 1041-1053.
@article{4068709f41474e3f9b207c024a0baf70,
title = "A sign-changing solution for a superlinear Dirichlet problem",
abstract = "We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the sign-changing solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].",
keywords = "Deformation lemma, Dirichlet problem, Sign-changing solution, Subcritical, Superlinear",
author = "Alfonso Castro and Jorge Cossio and Neuberger, {John M.}",
year = "1997",
month = "9",
language = "English (US)",
volume = "27",
pages = "1041--1053",
journal = "Rocky Mountain Journal of Mathematics",
issn = "0035-7596",
publisher = "Rocky Mountain Mathematics Consortium",
number = "4",

}

TY - JOUR

T1 - A sign-changing solution for a superlinear Dirichlet problem

AU - Castro, Alfonso

AU - Cossio, Jorge

AU - Neuberger, John M.

PY - 1997/9

Y1 - 1997/9

N2 - We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the sign-changing solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].

AB - We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the sign-changing solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].

KW - Deformation lemma

KW - Dirichlet problem

KW - Sign-changing solution

KW - Subcritical

KW - Superlinear

UR - http://www.scopus.com/inward/record.url?scp=0031372470&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031372470&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031372470

VL - 27

SP - 1041

EP - 1053

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

SN - 0035-7596

IS - 4

ER -