Non-existence of nodal and one-signed solutions for nonlinear variational equations with special symmetries
type: Item
instance of: scholarly article
title: Non-existence of nodal and one-signed solutions for nonlinear variational equations with special symmetries
zbMATH Open document ID: 0820.34013
DOI: 10.1007/BF00381162
author: Roberta Filippucci
author: Roberto Ghiselli Ricci
published in: Archive for Rational Mechanics and Analysis
publication date: 1995-09-06T00:00:00Z
review text: In a recent paper with \textit{P. Pucci} [Arch. Ration. Mech. Anal. 127, No. 3, 255-280 (1994; see the review above)], the authors established a lower bound of the length of the interval \((a, b)\) for which a one-signed solution \(u\) of equation \((| u'|^{m- 2} u')'+ f(t, u)= Q(t, u, u')\), \(m> 1\), \(t\in (a, b)\subset \mathbb{R}^ +\), with \(u(b)= u'(a)= 0\), exists. The purpose of this paper is to extend such a result to the much wider class of equations of the form \((G_ p(u'))'+ f(t, u)= Q(t, u, u')\). The results are applied to obtain non-existence theorems for nodal and one-signed solutions of the variational problem \((g(t) G_ p(u'))'+ g(t) f(u)= 0\), \(u(0)\neq 0\), \(u(T)= 0\), \(T> 0\), when \(T\) is sufficiently small.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 687682
zbMATH Keywords: one-signed solution
zbMATH Keywords: non-existence
zbMATH Keywords: variational problem
reviewed by: Radu Precup
MaRDI profile type: Publication
cites work: Q3472491
cites work: Elementary proof of the nonexistence of nodal solutions for the semilinear elliptic equations with critical sobolev exponent
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full work available at URL: https://doi.org/10.1007/bf00381162
OpenAlex ID: W2010164211
description: scientific article; zbMATH DE number 687682