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Open Access Research

Minimization of eigenvalues for some differential equations with integrable potentials

Gang Meng

Author Affiliations

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

Boundary Value Problems 2013, 2013:220  doi:10.1186/1687-2770-2013-220

Published: 7 November 2013

Abstract

In this paper we use the limiting approach to solve the minimization problem of the Dirichlet eigenvalues of Sturm-Liouville equations when the <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/220/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/220/mathml/M2">View MathML</a> norm of integrable potentials is given. The construction of an approximating problem in this paper can simplify the analysis in the limiting process.

MSC: 34L15, 34L40.

Keywords:
eigenvalue; Sturm-Liouville equations; minimization problem; integrable potential; <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/220/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/220/mathml/M2">View MathML</a> ball