Multiplicity results for superquadratic Dirichlet boundary value problems in \(\mathbb R^2\)
type: Item
instance of: scholarly article
title: Multiplicity results for superquadratic Dirichlet boundary value problems in \(\mathbb R^2\)
zbMATH Open document ID: 1152.34009
author: Anna Capietto
author: Walter Dambrosio
published in: Topological Methods in Nonlinear Analysis
publication date: 2008-08-12T00:00:00Z
review text: The authors consider with the boundary value problem of the form \[ z'=J\nabla F(t, z), \quad z=(x,y)\in \mathbb{R}^2,\;t\in [0,\pi], \qquad x(0)=0=x(\pi), \] where \(J\) is the standard symplectic matrix and \(F\in C^2([0,\pi]\times \mathbb{R}^2; R^+)\) satisfies \(\nabla F(t, 0)=0\) for \(t\in [0,\pi]\). They prove the existence of infinitely many solutions in the case when \(F\) has a superquadratic growth. The main result is based on a global bifurcation theorem obtained by \textit{A. Capietto} and \textit{W. Walter} [J. Differ. Equations 227, No. 2, 692--713 (2006; Zbl 1106.34006)].
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 5310040
zbMATH Keywords: symplectic matrix
zbMATH Keywords: superquadratic growth
zbMATH Keywords: global bifurcation theorem
zbMATH Keywords: infinitely solutions
reviewed by: Ruyun Ma
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5310040